A. A. Karatsuba, “On the distance between consecutive zeros of the Riemann zeta function that lie on the critical line”, Number theory, mathematical analysis, and their applications, Collection of articles. Dedicated to I. M. Vinogradov, a member of the Academy of Sciences on the occasion of his 90-birthday, Trudy Mat. Inst. Steklov., 157, 1981, 49–63; Proc. Steklov Inst. Math., 157 (1983), 51

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Trudy Matematicheskogo Instituta im. V. A. Steklova, 1981, Volume 157, Pages 49–63 (Mi tm2392)

This article is cited in 16 scientific papers (total in 18 papers)

On the distance between consecutive zeros of the Riemann zeta function that lie on the critical line

A. A. Karatsuba

Full-text PDF (1222 kB) Citations (18)

Bibliographic databases:

Document Type: Article

UDC: 511

Language: Russian

Citation: A. A. Karatsuba, “On the distance between consecutive zeros of the Riemann zeta function that lie on the critical line”, Number theory, mathematical analysis, and their applications, Collection of articles. Dedicated to I. M. Vinogradov, a member of the Academy of Sciences on the occasion of his 90-birthday, Trudy Mat. Inst. Steklov., 157, 1981, 49–63; Proc. Steklov Inst. Math., 157 (1983), 51–66

Citation in format AMSBIB

\Bibitem{Kar81}

\by A.~A.~Karatsuba

\paper On the distance between consecutive zeros of the Riemann zeta function that lie on the critical line

\inbook Number theory, mathematical analysis, and their applications

\bookinfo Collection of articles. Dedicated to I.\,M.~Vinogradov, a~member of the Academy of Sciences on the occasion of his 90-birthday

\serial Trudy Mat. Inst. Steklov.

\yr 1981

\vol 157

\pages 49--63

\mathnet{http://mi.mathnet.ru/tm2392}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=651758}

\zmath{https://zbmath.org/?q=an:0472.10040|0518.10045}

\transl

\jour Proc. Steklov Inst. Math.

\yr 1983

\vol 157

\pages 51--66

Linking options:

https://www.mathnet.ru/eng/tm2392

https://www.mathnet.ru/eng/tm/v157/p49

This publication is cited in the following 18 articles:

Sh. A. Khairulloev, “O veschestvennykh nulyakh proizvodnoi funktsii Khardi”, Chebyshevskii sb., 22:5 (2021), 234–240
Sh. A. Khairulloev, “O nulyakh funktsii Khardi i ee proizvodnykh, lezhaschikh na kriticheskoi pryamoi”, Chebyshevskii sb., 20:4 (2019), 371–384
M. A. Korolev, “On Rieman–Siegel formula for the derivatives of Hardy's function”, St. Petersburg Math. J., 29:4 (2018), 581–601
Matti Jutila, “An approximate functional equation for the primitive of Hardy's function”, Proc. Steklov Inst. Math., 299 (2017), 109–116
Do Dyk Tam, “O nulyakh dzeta-funktsii Rimana $\zeta(s)$ , lezhaschikh na pochti vsekh korotkikh promezhutkakh kriticheskoi pryamoi”, Chebyshevskii sb., 17:1 (2016), 71–89
A. A. Karatsuba, “Moskovskii doklad: teorema o priblizhenii trigonometricheskoi summy bolee korotkoi (ATS)”, Chebyshevskii sb., 16:1 (2015), 6–18
Do Dyk Tam, “Raspredelenie nulei, lezhaschikh na kriticheskoi pryamoi, lineinykh kombinatsii $L$ -funktsii Dirikhle”, Chebyshevskii sb., 16:3 (2015), 183–208
Proc. Steklov Inst. Math., 276 (2012), 149–155
S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22
I. S. Rezvyakova, “Zeros of the derivatives of the Riemann $\xi$ -function”, Izv. Math., 69:3 (2005), 539–605
A. A. Karatsuba, “Zeros and Local Extrema of Trigonometric Sums”, Problems Inform. Transmission, 39:1 (2003), 78–91
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)”, Russian Math. Surveys, 53:2 (1998), 419–422
S. A. Gritsenko, “Estimates of trigonometric sums by the third derivative”, Math. Notes, 60:3 (1996), 283–287
A. A. Karatsuba, “The distribution of prime numbers”, Russian Math. Surveys, 45:5 (1990), 99–171
L. V. Kiseleva, “On the number of zeros of the function $\zeta(s)$ on “almost all” short intervals of the critical line”, Math. USSR-Izv., 32:3 (1989), 475–499
A. A. Karatsuba, “On the real zeros of the function $\zeta(1/2+it)$ ”, Russian Math. Surveys, 40:4 (1985), 191–192
A. A. Karatsuba, “The Riemann zeta function and its zeros”, Russian Math. Surveys, 40:5 (1985), 23–82
A. A. Karatsuba, “On the zeros of the function $\zeta(s)$ on short intervals of the critical line”, Math. USSR-Izv., 24:3 (1985), 523–537

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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