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EXPONENTIAL MOMENTS OF THE ARGUMENT OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE
Author(s) -
Najnudel Joseph
Publication year - 2020
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12031
Subject(s) - mathematics , critical line , riemann zeta function , riemann xi function , logarithm , exponential function , riemann hypothesis , z function , particular values of riemann zeta function , line (geometry) , mathematical analysis , exponential decay , function (biology) , explicit formulae , arithmetic zeta function , pure mathematics , mathematical physics , prime zeta function , quantum mechanics , physics , geometry , evolutionary biology , biology , thermodynamics
Abstract In this article, we give, under the Riemann hypothesis, an upper bound for the exponential moments of the imaginary part of the logarithm of the Riemann zeta function on the critical line. Our result, which gives information on the fluctuations of the distribution of the zeros of ζ, has the same accuracy as the result obtained by Soundararajan ( Ann. of Math. (2) 170 (2) (2009), 981–993) for the moments of | ζ | .