On large values of the Riemann zeta-function on short segments of the critical line

DOI10.4064/aa166-4-3zbMath1377.11093arXiv1404.6649OpenAlexW3103099641MaRDI QIDQ2931772

M. A. Korolev

Publication date: 27 November 2014

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.6649

zbMATH Keywords

Riemann zeta functioncritical lineGram's lawargument of the Riemann zeta-function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (6)

On the horizontal distribution of zeros of the functions \(\operatorname{Re}\zeta(s)\) and \(\operatorname{Im}\zeta(s)\) ⋮ An extreme values of the function \(S(T)\) in short intervals ⋮ On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s ⋮ On the multiplicities of zeros of \(\zeta(s)\) and its values over short intervals ⋮ On Titchmarsh's phenomenon in the theory of the Riemann zeta function ⋮ Trigonometric series with noninteger harmonics

Uses Software

• ZetaGrid

Cites Work

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• Zero multiplicity and lower bound estimates of \(|\zeta(S)|\)
• Concerning the Karatsuba conjectures.
• Lower bounds for the maximum modulus of \(\zeta(s)\) in small domains of the critical strip.
• Lower bounds for the Riemann zeta-function on the critical line
• Approximate formulas for some functions of prime numbers
• On the Riemann zeta‐function ζ( s )—Gaps between sign changes of S ( t )
• The large values of the Riemann Zeta‐function
• Lower bounds for the maximum modulus of the Riemann zeta function on short segments of the critical line
• On the Distribution of Zeros of the Riemann Zeta-Function

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