Perturbed moments and a longer mollifier for critical zeros of \(\zeta \)

DOI10.1007/s40993-018-0103-4zbMath1444.11170arXiv1706.04593OpenAlexW2625351920MaRDI QIDQ2316155

Nicolas Robles, Kyle Pratt

Publication date: 26 July 2019

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.04593

zbMATH Keywords

zerosRiemann zeta-functioncritical lineWeil boundmollifierbilinear Kloosterman sumincomplete Kloosterman sumsconvolution structuretype I and type II sums

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) (zeta (s)) and (L(s, chi)) (11M06) Gauss and Kloosterman sums; generalizations (11L05) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Sums over arbitrary intervals (11L26)

Related Items (8)

On mean values of mollifiers and \(L\)-functions associated to primitive cusp forms ⋮ Real zeros of Hurwitz zeta-functions and their asymptotic behavior in the interval (0,1) ⋮ Zeros of combinations of the Riemann \(\Xi\)-function and the confluent hypergeometric function on bounded vertical shifts ⋮ Zeros of normalized combinations of \(\xi^{(k)}(s)\) on \(\mathrm{Re}(s)=1/2\) ⋮ The twisted mean square and critical zeros of Dirichlet \(L\)-functions ⋮ More than five-twelfths of the zeros of \(\zeta\) are on the critical line ⋮ Lower bounds for discrete negative moments of the Riemann zeta function ⋮ UNEXPECTED AVERAGE VALUES OF GENERALIZED VON MANGOLDT FUNCTIONS IN RESIDUE CLASSES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a mollifier of the perturbed Riemann zeta-function
• Large gaps between consecutive zeros of the Riemann zeta-function
• A short proof of Levinson's theorem
• Zeros of the Riemann zeta function on the critical line
• Twisted second moments of the Riemann zeta-function and applications
• Kloosterman sums and Fourier coefficients of cusp forms
• Zeros of derivatives of Riemann's xi-function on the critical line
• Bilinear forms with Kloosterman fractions
• Trilinear forms with Kloosterman fractions
• More than one third of zeros of Riemann's zeta-function are on \(\sigma=1/2\)
• The mean square of the product of the Riemann zeta-function with Dirichlet polynomials
• Gaps between zeros of \({\zeta}(s)\) and the distribution of zeros of \(\zeta'(s)\)
• On mean values of mollifiers and \(L\)-functions associated to primitive cusp forms
• Critical zeros of Dirichlet L-functions
• THE CONJECTURE IMPLIES THE RIEMANN HYPOTHESIS
• More than 41% of the zeros of the zeta function are on the critical line
• Power mean-values for Dirichlet's polynomials and the Riemann zeta-function, II
• More than two fifths of the zeros of the Riemann zeta function are on the critical line.
• Prime Numbers in Short Intervals and a Generalized Vaughan Identity
• Large gaps between zeros of the zeta‐function
• On Some Exponential Sums

This page was built for publication: Perturbed moments and a longer mollifier for critical zeros of \(\zeta \)