Further exploration of Riemann's functional equation

DOI10.7153/jca-11-02zbMath1424.11124arXiv1609.04795OpenAlexW2523587962MaRDI QIDQ4627842

Michael S. Milgram

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.04795

zbMATH Keywords

zeta functionRiemann hypothesiszeros of zeta functionRiemann's functional equationargument of derivative of zeta functionargument of zeta function

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) (zeta (s)) and (L(s, chi)) (11M06) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Elementary classical functions (33B99) Other special orthogonal polynomials and functions (33C47) Zeta and (L)-functions: analytic theory (11M99) Elementary functions (26A09) Analytic continuation of functions of one complex variable (30B40) Computational aspects of special functions (33F99)

Related Items (2)

An integral equation for Riemann's zeta function and its approximate solution ⋮ Uncovering functional relationships at zeros with special reference to Riemann's Zeta Function

Uses Software

• Maple
• DLMF

Cites Work

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• Integral and series representations of Riemann's zeta function and Dirichlet's eta function and a medley of related results
• An inequality for the Riemann zeta function
• Zeros of \(\zeta '(s)\) and the Riemann hypothesis
• On the Horizontal Monotonicity of |Γ(s)|
• Exploring Riemann’s functional equation

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