At least two fifths of the zeros of the Riemann zeta function are on the critical line

DOI10.1090/S0273-0979-1989-15704-2zbMath0668.10043OpenAlexW2116122835MaRDI QIDQ3820692

John Brian Conrey

Publication date: 1989

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1989-15704-2

zbMATH Keywords

Riemann zeta functionmollifierzeros on the critical lineaverages of Kloosterman sumsLevinson's method

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Trigonometric and exponential sums (general theory) (11L03)

Related Items (4)

Applications of theL-functions ratios conjectures ⋮ An explicit density estimate for Dirichlet $L$-series ⋮ On a theorem of Landau. II ⋮ Explicit zero density estimate for the Riemann zeta-function near the critical line

Cites Work

• Kloosterman sums and Fourier coefficients of cusp forms
• Zeros of derivatives of Riemann's xi-function on the critical line
• More than one third of zeros of Riemann's zeta-function are on \(\sigma=1/2\)
• More than two fifths of the zeros of the Riemann zeta function are on the critical line.
• Simple Zeros of the Riemann Zeta-Function on the Critical Line
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