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Uspekhi Mat. Nauk, 2006, Volume 61, Issue 3(369), Pages 3–92 (Mi umn1741)  

This article is cited in 24 scientific papers (total in 24 papers)

Behaviour of the argument of the Riemann zeta function on the critical line

A. A. Karatsubaa, M. A. Korolevb

a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Theorems on the number of zeros of the Riemann zeta function in quadrangles of small height that are placed to the right of the critical line are proved and used to prove theorems on the behaviour of the argument of the zeta function on the critical line.

DOI: https://doi.org/10.4213/rm1741

Full text: PDF file (990 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2006, 61:3, 389–482

Bibliographic databases:

Document Type: Article
UDC: 511
MSC: Primary 11M06; Secondary 11M26
Received: 15.01.2006

Citation: A. A. Karatsuba, M. A. Korolev, “Behaviour of the argument of the Riemann zeta function on the critical line”, Uspekhi Mat. Nauk, 61:3(369) (2006), 3–92; Russian Math. Surveys, 61:3 (2006), 389–482

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    This publication is cited in the following articles:
    1. M. A. Korolev, “On large distances between consecutive zeros of the Riemann zeta-function”, Izv. Math., 72:2 (2008), 291–304  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. M. A. Korolev, “Selberg's conjecture concerning the distribution of imaginary parts of zeros of the Riemann zeta function”, Dokl. Math., 78:1 (2008), 531–534  crossref  mathscinet  zmath  isi  elib  elib
    3. M. A. Korolev, “Gram's law and Selberg's conjecture on the distribution of zeros of the Riemann zeta function”, Izv. Math., 74:4 (2010), 743–780  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. R. N. Boyarinov, “On large distances between neighbouring zeros of the Riemann zeta-function”, Discrete Math. Appl., 20:4 (2010), 411–420  mathnet  crossref  crossref  mathscinet  elib  elib
    5. Boyarinov R.N., “Izmenenie znaka funktsii $S(T)$ na korotkikh intervalakh”, Vestn. Mosk. un-ta. Ser. 1: Matem. Mekh., 2010, no. 3, 51–53  elib
    6. Boyarinov R.N., “On the rate of convergence of distributions of random variables”, Dokl. Math., 82:3 (2010), 896–898  crossref  mathscinet  zmath  isi  elib  elib
    7. R. N. Boyarinov, “Argument dzeta-funktsii Rimana”, Chebyshevskii sb., 11:1 (2010), 54–67  mathnet  mathscinet
    8. Boyarinov R.N., “On fractional moments of random variables”, Dokl. Math., 83:1 (2011), 53–55  crossref  mathscinet  zmath  isi  elib  elib
    9. Boyarinov R.N., “On the value distribution of the Riemann zeta-function”, Dokl. Math., 83:3 (2011), 290–292  crossref  mathscinet  zmath  isi  elib  elib
    10. Boyarinov R.N., “Omega-theorems in the theory of the Riemann zeta function”, Dokl. Math., 83:3 (2011), 314–315  crossref  mathscinet  zmath  isi  elib  elib
    11. Trudgian T., “On the success and failure of Gram's law and the Rosser rule”, Acta Arith., 148:3 (2011), 225–256  crossref  mathscinet  zmath  isi  elib
    12. Boyarinov R.N., “O skorosti skhodimosti k predelnomu raspredeleniyu”, Vestn. Mosk. un-ta. Ser. 1. Matem. Mekh., 2011, no. 2, 19–27  mathscinet  elib
    13. R. N. Boyarinov, “Probabilistic methods in the theory of the Riemann zeta-function”, Theory Probab. Appl., 56:2 (2011), 181–192  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    14. M. A. Korolev, “On Gram's law in the theory of the Riemann zeta function”, Izv. Math., 76:2 (2012), 275–309  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. M. A. Korolev, “On Karatsuba's problem related to Gram's law”, Proc. Steklov Inst. Math., 276 (2012), 156–166  mathnet  crossref  mathscinet  isi
    16. R. N. Boyarinov, “On the number of Gram's intervals containing the ordinates of successive zeros of the Riemann zeta function”, Discrete Math. Appl., 22:5-6 (2012), 683–692  mathnet  crossref  crossref  mathscinet  elib
    17. V. Kargin, “On fluctuations of Riemann’s zeta zeros”, Probab. Theory Relat. Fields, 2012  crossref  mathscinet  isi
    18. Korolev M., “Gram's Law and the Argument of the Riemann Zeta Function”, Publ. Inst. Math.-Beograd, 92:106 (2012), 53–78  crossref  mathscinet  zmath  isi
    19. M. A. Korolev, “Moments of trigonometric polynomials and their applications in the theory of the Riemann zeta-function”, Dokl. Math, 89:3 (2014), 305  crossref  mathscinet  isi
    20. M. A. Korolev, “On the Horizontal Distribution of Zeros of the Functions $\operatorname{Re} \zeta(s)$ and $\operatorname{Im}\zeta(s)$”, Math. Notes, 98:6 (2015), 986–989  mathnet  crossref  crossref  mathscinet  isi  elib
    21. M. A. Korolev, “Gram's law in the theory of the Riemann zeta-function. Part 1”, Proc. Steklov Inst. Math., 292, suppl. 2 (2016), S1–S146  mathnet  crossref  crossref  isi  elib  elib
    22. M. A. Korolev, “Gram's Law in the Theory of Riemann Zeta-Function. Part 2”, Proc. Steklov Inst. Math., 294, suppl. 1 (2016), 1–78  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    23. Korolev M.A., “An extreme values of the function S(T) in short intervals”, Indian J. Pure Appl. Math., 47:4 (2016), 603–615  crossref  mathscinet  isi  scopus
    24. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  elib
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