Twisted second moments of the Riemann zeta-function and applications

DOI10.1016/j.jmaa.2015.08.064zbMath1383.11103OpenAlexW2196190165MaRDI QIDQ890502

Nicolas Robles, Arindam Roy, Alexandru Zaharescu

Publication date: 10 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.08.064

zbMATH Keywords

Riemann zeta-functionmollifierzeros on critical linetwisted second moment

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) Dirichlet series, exponential series and other series in one complex variable (30B50)

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Cites Work

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• A short proof of Levinson's theorem
• Zeros of the Riemann zeta function on the critical line
• Kloosterman sums and Fourier coefficients of cusp forms
• Zeros of derivatives of Riemann's xi-function on the critical line
• Zeros of derivatives of Riemann's Xi-function on the critical line. II
• More than one third of zeros of Riemann's zeta-function are on \(\sigma=1/2\)
• More than 41% of the zeros of the zeta function are on the critical line
• A simpler proof of Levinson's theorem
• 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.

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