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Shidlovskii, Andrei Borisovich
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Total publications: 46
Scientific articles: 34

Number of views:
This page:1420
Abstract pages:13704
Full texts:6245
References:948
Professor
Doctor of physico-mathematical sciences (1960)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 13.08.1915
Keywords: diophantine approximations; transcendental numbers.

Subject:

The problem to prove the algebraic independence of values at algebraic points of a set of Siegel's E-functions, which constitutes a solution of system of linear differential equations with coefficients from $C(z)$ and which consists of functions, algebraically independent over $C(z)$, is solved. In the case of the algebraic dependence over $C(z)$ of the considered E-functions a general theorem on the transcendence degree of the set of values of these functions at algebraic points is established. Theorems about the algebraic independence of subsets of the set of these values are proved. Lower bounds for the moduli of linear forms and polynomials with integer coefficients in the values of the considered E-functions are found. The general theorems are applied to a series of concrete subsets of E-functions.

Biography

Graduated from the Faculty of Mathematics of M. V. Lomonosov Moscow State University in 1950 (department of theory of numbers). Ph.D. thesis was defended in 1954. D.Sci. thesis was defended in 1960. A list of my works contains 100 titles. Since 1968 together with some colleagues I supervise the research seminare in number theory in MSU.

I am a Merited Promoter of Science of the Russian federation since 1980. I am a Merited Professor of the Moscow State University since 1995.
   
Main publications:
  • Shidlovskii A. B. O kriterii algebraicheskoi nezavisimosti znachenii odnogo klassa tselykh funktsii // Izv. AN SSSR. Ser. matem. 1959. T. 23, # 1, s. 35–66.
  • Shidlovskii A. B. O transtsendentnosti i algebraicheskoi nezavisimosti znachenii E-funktsii, svyazannykh lyubym chislom algebraicheskikh uravnenii nad polem ratsionalnykh funktsii // Izv. AN SSSR. Ser. matem. 1962. T. 26, # 6, s. 877–910.
  • Shidlovskii A. B. K obschei teoreme ob algebraicheskoi nezavisimosti znachenii E-funktsii // DAN SSSR. 1966. T. 171, # 4, s. 810–813.
  • Shidlovskii A. B. Ob otsenkakh mnogochlenov ot znachenii E-funktsii // Matem. sb. 1981. T. 115 (157), # 1 (5), s. 3–39.

https://www.mathnet.ru/eng/person8459
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/198813

Publications in Math-Net.Ru Citations
2000
1. A. B. Shidlovskii, “Properties of Algebraic Equations on the Set of $E$-Functions over the Field of Rational Functions”, Mat. Zametki, 68:5 (2000),  761–770  mathnet  mathscinet  zmath  elib; Math. Notes, 68:5 (2000), 644–651  isi 1
1999
2. A. B. Shidlovskii, “Arithmetical properties of the values of $E$-functions”, Mat. Zametki, 66:3 (1999),  452–458  mathnet  mathscinet  zmath; Math. Notes, 66:3 (1999), 366–371  isi 2
1997
3. A. B. Shidlovskii, “On the algebraic independence of values of $E$-functions”, Trudy Mat. Inst. Steklova, 218 (1997),  439–443  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 218 (1997), 439–443 3
1996
4. A. B. Shidlovskii, “On criteria for the linear and algebraic dependence of values of $E$-functions at algebraic points”, Uspekhi Mat. Nauk, 51:2(308) (1996),  179–180  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:2 (1996), 347–348  isi  scopus 1
5. Yu. V. Nesterenko, A. B. Shidlovskii, “Linear independence of values of $E$-functions”, Mat. Sb., 187:8 (1996),  93–108  mathnet  mathscinet  zmath; Sb. Math., 187:8 (1996), 1197–1211  isi  scopus 18
6. A. B. Shidlovskii, “On the linear independence of values of $E$-functions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 4,  53–56  mathnet  mathscinet  zmath 1
1995
7. A. B. Shidlovskii, “Linear independence of values of $E$-functions related by a single algebraic equation over the field of rational functions”, Mat. Zametki, 58:5 (1995),  794–797  mathnet  mathscinet  zmath; Math. Notes, 58:5 (1995), 1241–1244  isi 2
1994
8. A. B. Shidlovskii, “On the linear independence of the values of $E$-functions at algebraic points”, Mat. Zametki, 55:2 (1994),  174–185  mathnet  mathscinet  zmath; Math. Notes, 55:2 (1994), 224–231  isi 7
9. A. B. Shidlovskii, “On algebraic independence of the values of $E$-functions connected by algebraic equations over the field of rational functions”, Trudy Mat. Inst. Steklov., 207 (1994),  369–376  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 207 (1995), 339–345 2
1993
10. A. B. Shidlovskii, “Transcendence of the values of $E$-functions that are solutions of second order linear differential equations”, Mat. Sb., 184:5 (1993),  75–84  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 79:1 (1994), 63–71  isi 2
1992
11. A. B. Shidlovskii, “On the transcendence of values of a subclass of $E$-functions”, Uspekhi Mat. Nauk, 47:4(286) (1992),  215–216  mathnet  mathscinet  zmath; Russian Math. Surveys, 47:4 (1992), 228–229  isi 1
1991
12. A. B. Shidlovskii, “On the algebraic independence of values of $E$-functions”, Uspekhi Mat. Nauk, 46:4(280) (1991),  175–176  mathnet  mathscinet  zmath; Russian Math. Surveys, 46:4 (1991), 201–202  isi 4
1989
13. A. B. Shidlovskii, “Algebraic independence of values of $E$-functions at algebraic points”, Mat. Zametki, 45:1 (1989),  115–122  mathnet  mathscinet  zmath; Math. Notes, 45:1 (1989), 78–83  isi 4
14. A. B. Shidlovskii, “A criterion for algebraic independence of the values of an $E$-function at algebraic points”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1989, no. 6,  17–21  mathnet  mathscinet  zmath 4
1987
15. A. B. Shidlovskii, “On the transcendence and algebraic independence of the values of some classes of analytic functions”, Trudy Mat. Inst. Steklov., 180 (1987),  232–234  mathnet  zmath; Proc. Steklov Inst. Math., 180 (1989), 275–276 1
16. A. B. Shidlovskii, “On the algebraic independence of values of $E$-functions at algebraic points”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 1,  30–33  mathnet  mathscinet  zmath 1
1983
17. A. B. Shidlovskii, “The basic lemma of the method of proof of algebraic independence of values of $E$ -functions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1983, no. 6,  94–98  mathnet  mathscinet  zmath 1
1981
18. A. B. Shidlovskii, “On estimates for polynomials in values of $E$-functions”, Mat. Sb. (N.S.), 115(157):1(5) (1981),  3–39  mathnet  mathscinet  zmath; Math. USSR-Sb., 43:1 (1982), 1–32 3
1980
19. A. B. Shidlovskii, “On the arithmetic properties of values of $E$-functions connected by algebraic equations in the rational function field”, Dokl. Akad. Nauk SSSR, 251:4 (1980),  808–812  mathnet  mathscinet  zmath 2
20. A. B. Shidlovskii, “A bound for the measure of the mutual transcendence of values of $E$-functions connected by arbitrary algebraic equations over $\mathbb{C}(z)$”, Uspekhi Mat. Nauk, 35:2(212) (1980),  227–228  mathnet  mathscinet  zmath; Russian Math. Surveys, 35:2 (1980), 257–258  isi 1
1979
21. A. B. Shidlovskii, “On arithmetic properties of the values of E-functions at algebraic points”, Dokl. Akad. Nauk SSSR, 248:1 (1979),  50–55  mathnet  mathscinet  zmath 3
1973
22. A. B. Shidlovskii, “On arithmetic properties of values of analytic functions”, Trudy Mat. Inst. Steklov., 132 (1973),  169–202  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 132 (1973), 193–233 3
1970
23. N. I. Fel'dman, A. B. Shidlovskii, “The methods of A. O. Gelfond in the theory of transcendental numbers”, Uspekhi Mat. Nauk, 25:1(151) (1970),  201–202  mathnet  mathscinet  zmath 2
1968
24. A. B. Šidlovskiĭ, “Algebraic independence of the values of certain hypergeometric $E$-functions”, Tr. Mosk. Mat. Obs., 18 (1968),  55–64  mathnet  mathscinet  zmath 5
1967
25. A. B. Shidlovskii, “Transcendence measure estimates for the values of $E$-functions”, Mat. Zametki, 2:1 (1967),  33–44  mathnet  mathscinet  zmath; Math. Notes, 2:1 (1967), 508–513 8
26. A. B. Shidlovskii, “On estimates of the measure of transcendentality of the values of $E$-functions”, Uspekhi Mat. Nauk, 22:3(135) (1967),  245–246  mathnet  mathscinet 4
27. N. I. Fel'dman, A. B. Shidlovskii, “The development and present state of the theory of transcendental numbers”, Uspekhi Mat. Nauk, 22:3(135) (1967),  3–81  mathnet  mathscinet  zmath; Russian Math. Surveys, 22:3 (1967), 1–79 17
1966
28. A. B. Shidlovskii, “On a general theorem on the algebraic independence of values of $E$-functions”, Dokl. Akad. Nauk SSSR, 171:4 (1966),  810–813  mathnet  mathscinet  zmath 6
29. A. B. Shidlovskii, “Transcendence and algebraic independence of values of $E$-functions satisfying linear nonhomogeneous differential equations of the second order”, Dokl. Akad. Nauk SSSR, 169:1 (1966),  42–45  mathnet  mathscinet  zmath 7
1962
30. A. B. Shidlovskii, “Transcendency and algebraic independence of values of $E$-functions related by an arbitrary number of algebraic equations over the field of rational functions”, Izv. Akad. Nauk SSSR Ser. Mat., 26:6 (1962),  877–910  mathnet  mathscinet  zmath 9
1961
31. A. B. Shidlovskii, “A generalization of Lindemann's theorem”, Dokl. Akad. Nauk SSSR, 138:6 (1961),  1301–1304  mathnet  mathscinet  zmath 2
1959
32. A. B. Shidlovskii, “A criterion for algebraic independence of the values of a class of entire functions”, Izv. Akad. Nauk SSSR Ser. Mat., 23:1 (1959),  35–66  mathnet  mathscinet  zmath 23
33. A. B. Shidlovskii, “Transcendentality and algebraic independence of the values of certain functions”, Tr. Mosk. Mat. Obs., 8 (1959),  283–320  mathnet  mathscinet  zmath 14
34. A. B. Shidlovskii, “Transcendence and algebraic independence of the values of entire functions of certain classes”, Uch. Zap. Mosk. Gos. Univ., 186 (1959),  11–70  mathnet  mathscinet  zmath 8
1998
35. G. I. Arkhipov, V. I. Blagodatskikh, V. S. Vladimirov, S. M. Voronin, O. B. Lupanov, E. F. Mishchenko, Yu. V. Prokhorov, V. N. Chubarikov, A. B. Shidlovskii, “Anatolii Alekseevich Karatsuba (on his 60th birthday)”, Uspekhi Mat. Nauk, 53:2(320) (1998),  173–176  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:2 (1998), 419–422  isi 4
36. 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)”, Uspekhi Mat. Nauk, 53:1(319) (1998),  202–206  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:1 (1998), 199–204  isi 1
1995
37. N. M. Korobov, Yu. V. Nesterenko, A. B. Shidlovskii, “Naum Il'ich Feld'man (obituary)”, Uspekhi Mat. Nauk, 50:6(306) (1995),  157–162  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:6 (1995), 1247–1252  isi 1
38. A. I. Aptekarev, V. A. Kalyagin, V. V. Kozlov, M. K. Potapov, V. N. Sorokin, P. L. Ul'yanov, A. T. Fomenko, A. B. Shidlovskii, “Yevgeny Mikhailovich Nikishin”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 6,  110–111  mathnet  mathscinet  zmath 2
39. Yu. V. Nesterenko, A. B. Shidlovskii, “In memory of Naum Il'ich Fel'dman [1918–1994]”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 6,  108–109  mathnet  mathscinet  zmath 1
1991
40. I. P. Kubilis, V. I. Nechaev, S. B. Stechkin, A. B. Shidlovskii, “Aleksandr Adol'fovich Bukhshtab (obituary)”, Uspekhi Mat. Nauk, 46:1(277) (1991),  201–202  mathnet  mathscinet; Russian Math. Surveys, 46:1 (1991), 241–243  isi 1
1990
41. V. I. Arnol'd, A. G. Vitushkin, E. A. Gorin, V. Ya. Lin, Yu. V. Nesterenko, V. M. Tikhomirov, P. L. Ul'yanov, A. B. Shidlovskii, M. A. Shubin, “Vyacheslav Alekseevich Oleinikov (obituary)”, Uspekhi Mat. Nauk, 45:1(271) (1990),  163–165  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:1 (1990), 191–194  isi 2
1987
42. A. I. Aptekarev, V. V. Kozlov, A. M. Olevskii, M. K. Potapov, P. L. Ul'yanov, A. B. Shidlovskii, “In memory of Evgenij Mikhajlovich Nikishin”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 6,  88–91  mathnet  mathscinet  zmath 2
1984
43. A. I. Galochkin, N. I. Fel'dman, A. B. Shidlovskii, “All-Union conference “Theory of Transcendental Numbers and its Applications””, Uspekhi Mat. Nauk, 39:6(240) (1984),  251–252  mathnet 1
1975
44. S. B. Stechkin, R. V. Uzhdavinis, A. B. Shidlovskii, “All-Union Conference on Problems of Analytic Number Theory and Its Applications”, Uspekhi Mat. Nauk, 30:3(183) (1975),  198–200  mathnet 2
1967
45. I. I. Pyatetskii-Shapiro, A. B. Shidlovskii, “Aleksandr Osipovich Gel'fond (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 22:3(135) (1967),  247–256  mathnet  mathscinet  zmath; Russian Math. Surveys, 22:3 (1967), 234–242 1
1961
46. A. B. Shidlovskii, “Correction to the article “Transcendentality and algebraic independence of the values of certain functions” (Trudy Mosk. Matem. Ob-va 8(1959))”, Tr. Mosk. Mat. Obs., 10 (1961),  438  mathnet

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