Persons: Karatsuba, Anatolii Alekseevich

Persons

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

Karatsuba, Anatolii Alekseevich
(1937–2008)

Total publications:	179 (165)
in MathSciNet:	185 (175)
in zbMATH:	147 (140)
in Web of Science:	65 (56)
in Scopus:	79 (75)
Cited articles:	127
Citations:	1071
Presentations:	2

Number of views:
This page:	9452
Abstract pages:	68314
Full texts:	36972
References:	3879

Professor

Doctor of physico-mathematical sciences (1966)

Speciality:

01.01.06 (Mathematical logic, algebra, and number theory)

Birth date:

31.01.1937

Website:

https://www.mi.ras.ru/~karatsuba

Keywords:

analytic number theory, mathematical cybernetics.

Main publications:

A. A. Karatsuba, “The complexity of computations”, Proc. Steklov Inst. Math., 211 (1995), 169–183
A. A. Karatsuba, “On the zeros of the Davenport–Heilbronn function lying on the critical line”, Math. USSR-Izv., 36:2 (1991), 311–324
A. A. Karatsuba, “On the zeros of the function $\zeta(s)$ on short intervals of the critical line”, Math. USSR-Izv., 24:3 (1984), 523–537
A. A. Karatsuba, “Uniform approximation of the remainder term in the Dirichlet divisor problem”, Math. USSR-Izv., 6:3 (1972), 467–475
A. A. Karatsuba, “Sums of characters over prime numbers”, Math. USSR-Izv., 4:2 (1970), 303–326

https://www.mathnet.ru/eng/person8787

List of publications on Google Scholar

https://zbmath.org/authors/ai:karatsuba.anatolij-alekseevich

https://mathscinet.ams.org/mathscinet/MRAuthorID/193625

https://elibrary.ru/author_items.asp?authorid=2648

https://www.researchgate.net/profile/Anatolii_Karatsuba

Full list of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

Articles

1.	A. A. Karatsuba, “Five Lectures on the Life and Work of Academician I. M. Vinogradov”, Proc. Steklov Inst. Math., 314 (2021), 1–26
2.	A. A. Karatsuba, “Cosmology and zeta”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 11–17
3.	A. A. Karatsuba, “On zeros of certain Dirichlet series”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 6–10
4.	A. A. Karatsuba, “On local representation of zero by a form”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 1–5
5.	A. A. Karatsuba, “Vienna talk: on the number of zeros of the Riemann zeta function in short intervals of the critical line”, Chebyshevskii Sb., 16:1 (2015), 19–31
6.	A. A. Karatsuba, “Moscow talk: the theorem on approximation of trigonometric sum by a short one (ATS)”, Chebyshevskii Sb., 16:1 (2015), 6–18
7.	A. A. Karatsuba, “A property of the set of primes as a multiplicative basis of the natural numbers”, Dokl. Math., 84:1 (2011), 467–470
8.	A. A. Karatsuba, “A property of the set of prime numbers”, Russian Math. Surveys, 66:2 (2011), 209–220
9.	A. A. Karatsuba, E. A. Karatsuba, “Physical mathematics in number theory”, Funct. Anal. Other Math., 3:1 (2010)	5 ^[x]
10.	A. A. Karatsuba, E. A. Karatsuba, “On application of the functional equation of the Jacobi theta function to approximation of atomic inversion in the Jaynes-Cummings model”, Pacific Journal of Applied Mathematics, 2:3 (2010), 41–63
11.	A. A. Karatsuba, “New Estimates of Short Kloosterman Sums”, Math. Notes, 88:3 (2010), 347–359
12.	A. A. Karatsuba, E. A. Karatsuba, “A resummation formula for collapse and revival in the Jaynes–Cummings model”, J. Phys. A, 42:19 (2009), 195304 , 16 pp.	18 ^[x]
13.	A. A. Karatsuba, “Euler and Number Theory”, Proc. Steklov Inst. Math., 264 (2009), 74–86
14.	A. A. Karatsuba, E. A. Karatsuba, “Application of ATS in a quantum-optical model”, Analysis and mathematical physics, Trends Math., Birkhäuser Verlag, Basel, 2009, 211–232	5 ^[x]
15.	A. A. Karatsuba, E. A. Karatsuba, “The “problem of remainders” in theoretical physics: “physical zeta” function”, Proceedings of the 5th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physics (Institute of Physics, Belgrade, Serbia), eds. B. Dragovich and Z. Rakic, 2009, 197–210
16.	A. A. Karatsuba, “Nelineinye summy kharakterov s prostymi chislami”, Dokl. RAN, 421:2 (2008), 162–163	1 ^[x]
17.	A. A. Karatsuba, “Arithmetic problems in the theory of Dirichlet characters”, Russian Math. Surveys, 63:4 (2008), 641–690
18.	A. A. Karatsuba, “Euler and number theory”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), 169–179
19.	A. A. Karatsuba, M. A. Korolëv, “Priblizhenie trigonometricheskoi summy bolee korotkoi”, Dokl. RAN, 412:2 (2007), 159–161	1 ^[x]
20.	M. Z. Garaev , A. A. Karatsuba, “The representation of residue classes by products of small integers”, Proc. Edinb. Math. Soc. (2), 50:2 (2007), 363–375	11 ^[x]
21.	A. A. Karatsuba, M. A. Korolev, “A theorem on the approximation of a trigonometric sum by a shorter one”, Izv. Math., 71:2 (2007), 341–370
22.	A. A. Karatsuba, “Trigonometricheskie summy Korobova”, Chebyshevskii sb., 7:3(19) (2006), 101–109
23.	A. A. Karatsuba, “Zero multiplicity and lower bound estimates of $\|\zeta(s)\|$”, Funct. Approx. Comment. Math., 35 (2006), 195–207	7 ^[x]
24.	M. Z. Garaev , A. A. Karatsuba, “New estimates of double trigonometric sums with exponential functions”, Arch. Math. (Basel), 87:1 (2006), 33–40	7 ^[x]
25.	A. A. Karatsuba, M. A. Korolev, “Behaviour of the argument of the Riemann zeta function on the critical line”, Russian Math. Surveys, 61:3 (2006), 389–482
26.	A. A. Karatsuba, “O kolichestve peremen znaka funktsii $R_1(x)$ i eë srednikh znachenii”, Chebyshevskii sb., 6:2(14) (2005), 163–183
27.	A. A. Karatsuba, “Povedenie funktsii $R_1(x)$ i ee srednego znacheniya”, Dokl. RAN, 404:4 (2005), 439–442	2 ^[x]
28.	A. A. Karatsuba, “O priblizheniyakh $\pi(x)$”, Chebyshevskii sb., 5:4(12) (2005), 5–20
29.	M. Z. Garaev , A. A. Karatsuba, “On character sums and the exceptional set of a congruence problem”, J. Number Theory, 114:1 (2005), 182–192	10 ^[x]
30.	A. A. Karatsuba, M. A. Korolev, “The argument of the Riemann zeta function”, Russian Math. Surveys, 60:3 (2005), 433–488
31.	A. A. Karatsuba, “On the asymptotic Riemann formula for $\pi(x)$”, Dokl. RAN, 396:5 (2004), 595–596	1 ^[x]
32.	A. A. Karatsuba, “Lower bounds for the maximum modulus of the Riemann zeta function on short segments of the critical line”, Izv. Math., 68:6 (2004), 1157–1163
33.	A. A. Karatsuba, “Omega Theorems for Zeta Sums”, Math. Notes, 73:2 (2003), 212–217
34.	A. A. Karatsuba, “Zeros and Local Extrema of Trigonometric Sums”, Problems Inform. Transmission, 39:1 (2003), 78–91
35.	A. A. Karatsuba, “On zeros of trigonometric sums”, Dokl. RAN, 387:1 (2002), 11–12	3 ^[x]
36.	A. A. Karatsuba, “Fractional Moments and Zeros of $\zeta (s)$ on the Critical Line”, Math. Notes, 72:4 (2002), 466–472
37.	A. A. Karatsuba, “On lower bounds for the Riemann zeta function”, Dokl. RAN, 376:1 (2001), 15–16	6 ^[x]
38.	A. A. Karatsuba, “On fractional parts of rapidly growing functions”, Izv. Math., 65:4 (2001), 727–748
39.	A. A. Karatsuba, “Lower Bounds for the Maximum Modulus of $\zeta(s)$ in Small Domains of the Critical Strip”, Math. Notes, 70:5 (2001), 724–726
40.	A. A. Karatsuba, “On the Relationship between the Multidimensional Dirichlet Divisor Problem and the Boundary of Zeros of $\zeta(s)$”, Math. Notes, 70:3 (2001), 432–435
41.	A. A. Karatsuba, “Sums of characters with prime numbers and their applications”, Tatra Mt. Math. Publ., 20 (2000), 155–162
42.	A. A. Karatsuba, “The multidimensional Dirichlet divisor problem and zero free regions for the Riemann zeta function”, Funct. Approx. Comment. Math., 28 (2000), 131–140	4 ^[x]
43.	A. A. Karatsuba, “Weighted character sums”, Izv. Math., 64:2 (2000), 249–263
44.	A. A. Karatsuba, “Double Kloosterman sums”, Math. Notes, 66:5 (1999), 565–569
45.	A. A. Karatsuba, B. Novak, “Arithmetical problems with numbers of special type”, Math. Notes, 66:2 (1999), 251–253
46.	A. A. Karatsuba, “Regular sets modulo a given number”, Proceedings of the 13th Czech and Slovak International Conference on Number Theory (Ostravice, 1997), Acta Math. Inform. Univ. Ostraviensis, 6, no. 1, 1998, 129–134 (Russian)
47.	A. A. Karatsuba, “An estimate of the $L_1$-norm of an exponential sum”, Math. Notes, 64:3 (1998), 401–404
48.	A. A. Karatsuba, “Regular sets in residual classes”, Math. Notes, 64:2 (1998), 190–193
49.	A. A. Karatsuba, “Analogues of incomplete Kloosterman sums and their applications”, Tatra Mt. Math. Publ., 11 (1997), 89–120 (Russian)
50.	A. A. Karatsuba, “Additive congruences”, Izv. Math., 61:2 (1997), 317–329
51.	A. A. Karatsuba, “Sums of fractional parts of functions of a special form”, Dokl. Math., 54:1 (1996), 541
52.	A. A. Karatsuba, “On the function $S(t)$”, Izv. Math., 60:5 (1996), 901–931
53.	A. A. Karatsuba, “Density theorem and the behavior of the argument of the Riemann zeta function”, Math. Notes, 60:3 (1996), 333–334
54.	A. A. Karatsuba, “Analogues of Kloosterman sums”, Izv. Math., 59:5 (1995), 971–981
55.	A. A. Karatsuba, “Fractional parts of functions of a special form”, Izv. Math., 59:4 (1995), 721–740
56.	A. A. Karatsuba, “On a certain arithmetic function”, Russian Math. Surveys, 50:5 (1995), 1088–1089
57.	A. A. Karatsuba, “The complexity of computations”, Proc. Steklov Inst. Math., 211 (1995), 169–183
58.	A. A. Karatsuba, “Zeros of arithmetic Dirichlet series”, Math. Slovaca, 44:5 (1994), 633–649 (Russian)
59.	A. A. Karatsuba, “I. M. Vinogradov and his method of trigonometric sums”, Proc. Steklov Inst. Math., 207 (1995), 1–33
60.	A. A. Karatsuba, “A new approach to the problem of the zeros of some Dirichlet series”, Proc. Steklov Inst. Math., 207 (1995), 163–177
61.	Russian Acad. Sci. Dokl. Math., 48:3 (1994), 452–454
62.	A. A. Karatsuba, “On the zeros of arithmetic Dirichlet series without Euler product”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 193–203
63.	A. A. Karatsuba, “On the zeros of a class of functions generated by the Hurwitz function”, Russian Math. Surveys, 48:5 (1993), 175–176
64.	A. A. Karatsuba, “On zeros of the Davenport–Heilbronn function”, Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), Univ. Salerno, Salerno, 1992, 271–293
65.	Soviet Math. Dokl., 45:1 (1992), 46–47
66.	A. A. Karatsuba, “On the number of zeros of the Riemann zeta-function lying in almost all short intervals of the critical line”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 353–376
67.	A. A. Karatsuba, “A refinement of theorems on the number of zeros lying on intervals of the critical line of certain Dirichlet series”, Russian Math. Surveys, 47:2 (1992), 219–220
68.	V. S. Vladimirov, A. A. Karatsuba, I. R. Shafarevich, “On the centennial of the birth of Academician I. M. Vinogradov”, Vestn. Akademii nauk SSSR, 1991, no. 9, 91–103 (Russian)
69.	Soviet Math. Dokl., 44:1 (1992), 145–148
70.	A. A. Karatsuba, “On the zeros of Riemann's zeta-function on the critical line”, International Symposium in Memory of Hua Loo Keng (Beijing, 1988), v. I, Springer, Berlin, 1991, 117–162
71.	Soviet Math. Dokl., 43:2 (1991), 589–590
72.	A. A. Karatsuba, “On the zeros of a special type of function connected with Dirichlet series”, Math. USSR-Izv., 38:3 (1992), 471–502
73.	A. A. Karatsuba, “On density theorem”, Proc. Steklov Inst. Math., 200 (1993), 205–217
74.	A. A. Karatsuba, “On the zeros of the Davenport–Heilbronn function lying on the critical line”, Math. USSR-Izv., 36:2 (1991), 311–324
75.	A. A. Karatsuba, “The distribution of prime numbers”, Russian Math. Surveys, 45:5 (1990), 99–171
76.	A. A. Karatsuba, “Zeros of certain Dirichlet series”, Russian Math. Surveys, 45:1 (1990), 207–208
77.	A. A. Karatsuba, E. I. Kovalevskaya, \u{I}. P. Kubilyus, “Biography and scientific work of V. G. Sprindzhuk”, Acta Arith., 53:1 (1989), 5–16 (Russian)
78.	A. A. Karatsuba, “On a Diophantine inequality”, Acta Arith., 53:3 (1989), 309–324	3 ^[x]
79.	A. A. Karatsuba, “Approximation of exponential sums by shorter ones”, Proc. Indian Acad. Sci. Math. Sci., 97:1-3 (1987), 167–178 (1988)	16 ^[x]
80.	Soviet Math. Dokl., 36:1 (1988), 75–77
81.	A. A. Karatsuba, “The distribution of pairs of quadratic residues and nonresidues of a special form”, Math. USSR-Izv., 31:2 (1988), 307–323
82.	A. A. Karatsuba, “The Hilbert–Kamke problem in analytic number theory”, Math. Notes, 41:2 (1987), 155–161
83.	A. A. Karatsuba, “Zeros of the function $\zeta(\frac12+it)$”, Dokl. AN SSSR, 281:5 (1985), 1038–1041
84.	A. A. Karatsuba, “On the function $G(n)$ in Waring's problem”, Math. USSR-Izv., 27:2 (1986), 239–249
85.	A. A. Karatsuba, “The Riemann zeta function and its zeros”, Russian Math. Surveys, 40:5 (1985), 23–82
86.	A. A. Karatsuba, “On the real zeros of the function $\zeta(1/2+it)$”, Russian Math. Surveys, 40:4 (1985), 191–192
87.	A. A. Karatsuba, “Zeros of the Riemann zeta function on the critical line”, Proc. Steklov Inst. Math., 167 (1986), 187–200
88.	A. A. Karatsuba, “On the zeros of the function $\zeta(s)$ in the neighborhood of the critical line”, Math. USSR-Izv., 26:2 (1986), 307–313
89.	A. A. Karatsuba, “Quadratic residues and nonresidues in sparse sequences”, Dokl. AN SSSR, 279:5 (1984), 1044–1046	2 ^[x]
90.	A. A. Karatsuba, “Zeros of the Riemann zeta function”, Dokl. AN SSSR, 276:3 (1984), 535–539	2 ^[x]
91.	A. A. Karatsuba, “On the zeros of the function $\zeta(s)$ on short intervals of the critical line”, Math. USSR-Izv., 24:3 (1984), 523–537
92.	I. M. Vinogradov, A. A. Karatsuba, “The method of trigonometric sums in number theory”, Proc. Steklov Inst. Math., 168 (1986), 3–30
93.	A. A. Karatsuba, “Vinogradov's method of trigonometric sums”, Proc. Steklov Inst. Math., 163 (1985), 117–123
94.	A. A. Karatsuba, “The distribution of zeros of the function $\zeta(1/2+it)$”, Math. USSR-Izv., 25:3 (1985), 519–529
95.	A. A. Karatsuba, “Teoriya chisel”, Ocherki razvitiya matematiki v SSSR. Teoreticheskaya matematika. Prikladnye voprosy matematiki, Naukova dumka, Kiev, 1983, 106–133 (Russian)
96.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “New uniform estimates for multiple trigonometric sums”, Dokl. AN SSSR, 272:1 (1983), 11–12	1 ^[x]
97.	A. A. Karatsuba, “Zeros of the Riemann zeta function in short intervals of the critical line”, Dokl. AN SSSR, 272:6 (1983), 1312–1314	4 ^[x]
98.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Special cases of the theory of multiple trigonometric sums”, Math. USSR-Izv., 23:1 (1984), 17–82
99.	G. I. Arkhipov, A. A. Karatsuba, “On the representation of zero by a form in a $p$-adic number field”, Dokl. AN SSSR, 262:1 (1982), 11–13	1 ^[x]
100.	G. I. Arkhipov, A. A. Karatsuba, “A problem in the theory of congruences”, Russian Math. Surveys, 37:5 (1982), 157–158
101.	A. A. Karatsuba, “On a problem with prime numbers”, Dokl. AN SSSR, 259:6 (1981), 1291–1293	2 ^[x]
102.	G. I. Arkhipov, A. A. Karatsuba, “On local representation of zero by a form”, Math. USSR-Izv., 19:2 (1982), 231–240
103.	A. A. Karatsuba, “On the distance between consecutive zeros of the Riemann zeta function that lie on the critical line”, Proc. Steklov Inst. Math., 157 (1983), 51–66
104.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Uniform estimates of multiple trigonometric sums”, Dokl. AN SSSR, 252:6 (1980), 1289–1291	2 ^[x]
105.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “On a system of Diophantine equations”, Dokl. AN SSSR, 252:2 (1980), 275–276	1 ^[x]
106.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Multiple trigonometric sums and their applications”, Math. USSR-Izv., 17:1 (1981), 1–54
107.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Exponent of convergence of the singular integral in the Terry problem”, Dokl. AN SSSR, 248:2 (1979), 268–272	5 ^[x]
108.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Trigonometric integrals”, Math. USSR-Izv., 15:2 (1980), 211–239
109.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Distribution of fractional parts of polynomials in several variables”, Math. Notes, 25:1 (1979), 3–9
110.	A. A. Karatsuba, “Asymptotics of an arithmetic sum”, Math. Notes, 24:6 (1978), 893–895
111.	A. A. Karatsuba, “Distribution of the values of Legendre symbols in polynomials with prime numbers”, Dokl. AN SSSR, 238:3 (1978), 524–526	2 ^[x]
112.	G. I. Arkhipov, A. A. Karatsuba, “I. M. Vinogradov's integral”, Dokl. AN SSSR, 239:4 (1978), 764–765
113.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “A sharp estimate for the number of solutions of a system of Diophantine equations”, Math. USSR-Izv., 13:3 (1979), 461–497
114.	A. A. Karatsuba, “Sums of Legendre symbols of polynomials of second degree over prime numbers”, Math. USSR-Izv., 12:2 (1978), 299–308
115.	G. I. Arkhipov, A. A. Karatsuba, “A new estimate of an integral of I. M. Vinogradov”, Math. USSR-Izv., 13:1 (1979), 52–62
116.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “An upper bound of the modulus of a multiple trigonometric sum”, Proc. Steklov Inst. Math., 143 (1980), 1–31
117.	A. A. Karatsuba, “Distribution of values of nonprincipal characters”, Proc. Steklov Inst. Math., 142 (1979), 165–174
118.	A. A. Karatsuba, “A system of congruences”, Math. Notes, 19:3 (1976), 237–239
119.	A. A. Karatsuba, “Trigonometric sums and their applications”, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974), v. 1, Canad. Math. Congress, Montreal, Que., 1975, 365–368 (Russian)
120.	A. A. Karatsuba, “Some arithmetical problems with numbers having small prime divisors”, Collection of articles in memory of Juriĭ Vladimirovič Linnik, Acta Arith., 27 (1975), 489–492 (Russian)	4 ^[x]
121.	A. A. Karatsuba, “Some problems of contemporary analytic number theorem”, Math. Notes, 17:2 (1975), 195–199
122.	A. A. Karatsuba, “Sums of characters in sequences of shifted prime numbers, with applications”, Math. Notes, 17:1 (1975), 91–93
123.	A. A. Karatsuba, “On some problems of prime numbers theory, connected with I. M. Vinogradov's method”, Proc. Steklov Inst. Math., 132 (1973), 293–298
124.	A. A. Karatsuba, “The mean value of the modulus of a trigonometric sum”, Math. USSR-Izv., 7:6 (1973), 1199–1223
125.	A. A. Karatsuba, “Lower estimates of sums of polynomial characters”, Math. Notes, 14:1 (1973), 593–596
126.	A. A. Karatsuba, “The problem of Dirichlet divisors in number fields”, Dokl. AN SSSR, 204 (1972), 540–541	1 ^[x]
127.	A. A. Karatsuba, “Uniform approximation of the remainder term in the Dirichlet divisor problem”, Math. USSR-Izv., 6:3 (1972), 467–475
128.	A. A. Karatsuba, “Estimates of trigonometric sums by the method of I. M. Vinogradov, and their applications”, Proc. Steklov Inst. Math., 112 (1971), 251–265
129.	Soviet Math. Dokl., 12 (1971), 1172–1174
130.	A. A. Karatsuba, “Distribution of power residues and non-residues in additive squences.”, Dokl. AN SSSR, 196 (1971), 759–760	5 ^[x]
131.	A. A. Karatsuba, “Sums of characters with prime numbers in an arithmetic progression”, Math. USSR-Izv., 5:3 (1971), 485–501
132.	A. A. Karatsuba, “The distribution of products of shifted prime numbers in arithmetic progressions”, Dokl. AN SSSR, 192 (1970), 724–727	12 ^[x]
133.	A. A. Karatsuba, “Sums of characters with prime numbers”, Dokl. AN SSSR, 190 (1970), 517–518	6 ^[x]
134.	A. A. Karatsuba, “Estimates of character sums”, Math. USSR-Izv., 4:1 (1970), 19–29
135.	A. A. Karatsuba, “Sums of characters over prime numbers”, Math. USSR-Izv., 4:2 (1970), 303–326
136.	A. A. Karatsuba, “Trigonometric sums”, Dokl. AN SSSR, 189 (1969), 31–34	2 ^[x]
137.	A. A. Karatsuba, “Ob odnoi asimptoticheskoi formule (k shestidesyatiletiyu A. O. Gelfonda)”, Tr. MMO, 18, Izd-vo Mosk. un-ta, M., 1968, 77–82
138.	A. A. Karatsuba, “Sums of characters, and primitive roots, in finite fields”, Dokl. AN SSSR, 180 (1968), 1287–1289	14 ^[x]
139.	A. A. Karatsuba, “About a system of indeterminate equations”, Math. Notes, 4:1 (1968), 565–567
140.	A. A. Karatsuba, “Estimates of complete trigonometric sums”, Math. Notes, 1:2 (1967), 133–139
141.	A. A. Karatsuba, “Asymptotic formulae for a certain class of trigonometric sums”, Dokl. AN SSSR, 169 (1966), 9–11	2 ^[x]
142.	A. A. Karatsuba, “Theorems on the mean and complete trigonometric sums”, Izv. Akad. Nauk SSSR Ser. Mat., 30:1 (1966), 183–206
143.	A. A. Karatsuba, “On estimation of the number of solutions of certain equations”, Dokl. AN SSSR, 165 (1965), 31–32	2 ^[x]
144.	A. A. Karatsuba, “Congruence systems and equations of Waring type”, Dokl. AN SSSR, 165 (1965), 274–276	5 ^[x]
145.	A. A. Karatsuba, “On systems of congruences”, Izv. Akad. Nauk SSSR Ser. Mat., 29:4 (1965), 935–944
146.	A. A. Karatsuba, “Trigonometric sums of a special type and their applications”, Izv. Akad. Nauk SSSR Ser. Mat., 28:1 (1964), 237–248
147.	A. A. Karatsuba, N. M. Korobov, “A mean-value theorem”, Dokl. AN SSSR, 149 (1963), 245–248	3 ^[x]
148.	A. A. Karatsuba, “Waring's problem for a congruence modulo the power of a prime”, Vestnik Moskov. Univ. Ser. I Mat. Meh., 1962:4 (1962), 28–38
149.	A. A. Karatsuba, “Distribution of fractional parts of polynomials of a special type”, Vestnik Moskov. Univ. Ser. I Mat. Meh., 1962:3 (1962), 34–39
150.	A. A. Karatsuba, “An analogue of Waring's problem”, Vestnik Moskov. Univ. Ser. I Mat. Meh., 1962:1 (1962), 38–46
151.	A. A. Karatsuba, “Tarry's problem for a system of congruences”, Mat. Sb. (N.S.), 55(97):2 (1961), 209–220
152.	A. A. Karatsuba, “Solution to a problem in the theory of finite automatons”, Uspekhi Mat. Nauk, 15:3(93) (1960), 157–159
Books

153.	G. I. Arkhipov, V. N. Chubarikov, A. A. Karatsuba, Trigonometric sums in number theory and analysis, de Gruyter Expositions in Mathematics, 39, Walter de Gruyter GmbH & Co. KG, Berlin, 2004 , x+554 pp.
154.	A. A. Karatsuba, Complex analysis in number theory, CRC Press, Boca Raton, FL, 1995 , x+187 pp.
155.	S. M. Voronin, A. A. Karatsuba, Dzeta-funktsiya Rimana, Fizmatlit, M., 1994 , 376 pp.
156.	A. A. Karatsuba, Basic analytic number theory, Springer-Verlag, Berlin, 1993 , xiv+222 pp.
157.	A. A. Karatsuba, S. M. Voronin, The Riemann zeta-function, de Gruyter Expositions in Mathematics, 5, Walter de Gruyter & Co., Berlin, 1992 , xii+396 pp.
158.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987 , 368 pp.
159.	A. A. Karatsuba, Osnovy analiticheskoi teorii chisel, 2-e izd., Nauka, M., 1983 , 240 pp.
160.	G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Multiple trigonometric sums”, Proc. Steklov Inst. Math., 151:2 (1982), 1–126
161.	A. A. Karatsuba, Fundamentos de la teoría analítica de los números, Mir, M., 1979 , 245 pp. (Spanish)
162.	A. A. Karatsuba, Osnovy analiticheskoi teorii chisel, Nauka, M., 1975 , 183 pp.
Thesis

163.	A. A. Karatsuba, “The method of trigonometric sums and theorems of the mean”, Math. Notes, 1:1 (1967), 64–71
Information matherials

164.	A. A. Karatsuba, “All-Union Conference on Number Theory, dedicated to the centennial of I. M. Vinogradov”, Uspekhi Mat. Nauk, 47:2(284) (1992), 211
165.	D. I. Ismoilov, A. A. Karatsuba, S. A. Stepanov, “All-Union School-Seminar on number theory”, Uspekhi Mat. Nauk, 33:2(200) (1978), 234–236
Personalia

166.	A. A. Karatsuba, Š. Porubský, M. Rokyta, Z. Vlášek, “Prof. RNDr. Břetislav Novák, DrSc. (1938–2003) would be seventy”, Math. Bohem., 133:2 (2008), 209–218	1 ^[x]
167.	R. A. Arhontova, A. G. Baskakov, I. A. Bakhtin, E. S. Belyaeva, Yu. G. Borisovich, A. S. Grechenko, V. R. Zachepa, A. A. Karatsuba, A. F. Kudinov, V. V. Obukhovskii, A. I. Perov, A. S. Potapov, E. M. Semenov, V. P. Trofimov, N. N. Udodenko, “Kirill Andreevich Rodosskii (obituary)”, Russian Math. Surveys, 61:5 (2006), 971–973
168.	G. I. Arkhipov, A. I. Galochkin, G. Ya. Galin, A. A. Karatsuba, V. N. Latyshev, T. P. Lukashenko, O. B. Lupanov, Yu. N. Makarov, Yu. V. Nesterenko, M. K. Potapov, V. G. Chirskii, V. N. Chubarikov, “Andrei Borisovich Shidlovskii (on the occasion of his 90th birthday)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2006, no. 3, 68–70
169.	G. I. Arkhipov, V. G. Zhuravlev, V. A. Iskovskikh, A. A. Karatsuba, M. B. Levina-Khripunova, V. N. Chubarikov, A. A. Yudin, “Nikolai Mikhailovich Timofeev (obituary)”, Russian Math. Surveys, 58:4 (2003), 773–776
170.	G. I. Arkhipov, V. I. Blagodatskikh, A. A. Bolibrukh, V. A. Iskovskikh, A. A. Karatsuba, Yu. V. Prokhorov, A. T. Fomenko, V. N. Chubarikov, I. R. Shafarevich, “Sergei Mikhailovich Voronin (obituary)”, Russian Math. Surveys, 53:4 (1998), 777–781
171.	V. S. Vladimirov, A. A. Dezin, A. A. Karatsuba, L. D. Kudryavtsev, M. P. Mineev, S. M. Nikol'skii, L. P. Postnikova, Yu. V. Prokhorov, V. N. Chubarikov, A. B. Shidlovskii, A. A. Yudin, “Aleksei Georgievich Postnikov (obituary)”, Russian Math. Surveys, 53:1 (1998), 199–204
172.	B. M. Bredikhin, V. S. Vladimirov, A. A. Karatsuba, E. F. Mishchenko, S. M. Nikol'skii, “Aleksandr Fedorovich Lavrik (on his sixtieth birthday)”, Russian Math. Surveys, 43:4 (1988), 245–247
173.	V. I. Bernik, A. A. Karatsuba, I. P. Kubilyus, V. P. Platonov, D. A. Suprunenko, “Vladimir Gennadievich Sprindzhuk (obituary)”, Russian Math. Surveys, 43:4 (1988), 195–197
174.	B. M. Bredikhin, V. E. Voskresenskii, A. A. Karatsuba, A. F. Lavrik, A. V. Malyshev, A. G. Postnikov, V. G. Sprindzhuk, “Nikolai Grigor'evich Chudakov (obituary)”, Russian Math. Surveys, 42:5 (1987), 161–162
175.	A. A. Karatsuba, “Ivan Matveevich Vinogradov (on his ninetieth birthday)”, Russian Math. Surveys, 36:6 (1981), 1–17
Miscellaneous

176.	A. A. Karatsuba, “Comments to My Works,Written by Myself”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S1–S23
177.	Teoriya chisel i analiz, Sbornik statei. Trudy Mezhdunarodnoi konferentsii po teorii chisel, posvyaschennoi 100-letiyu so dnya rozhdeniya akademika I. M. Vinogradova, Tr. MIAN, 207, ed. E. F. Mischenko, A. A. Karatsuba, Nauka, M., 1994 , 384 pp.
178.	A. A. Karatsuba, Yu. P. Ofman, “Multiplication of multidigit numbers on automata”, Soviet Physics-Doklady, 7 (1963), 595–596
179.	A. A. Karatsuba, “Estimates of trigonometric sums of a special form, and their applications”, Dokl. AN SSSR, 137 (1961), 513–514

Presentations in Math-Net.Ru

1.	Euler and number theory A. A. Karatsuba Scientific conference "Leonhard Euler and Contemporary Mathematics" May 17, 2007
2.	Lower bounds and the multiplicity of a zero of the Riemann zeta-function A. A. Karatsuba Steklov Mathematical Institute Seminar January 18, 2007 16:00

Books in Math-Net.Ru

Number theory and analysis, Proceeding of the International Conference on number theory dedicated to the Centenary of I. M. Vinogradov, Trudy Mat. Inst. Steklov., 207, ed. E. F. Mishchenko, A. A. Karatsuba, 1994, 384 с.
http://mi.mathnet.ru/book1089
G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, Multiple trigonometric sums, Trudy Mat. Inst. Steklov., 151, ed. S. M. Nikol'skii, 1980, 128 с.
http://mi.mathnet.ru/book1189

Organisations

Registration to the website

Logotypes

Articles

Books

Thesis

Information matherials

Personalia

Miscellaneous