Uncovering functional relationships at zeros with special reference to Riemann's Zeta Function

DOI10.7153/jca-2018-12-04zbMath1424.11127arXiv1505.06515OpenAlexW3100738929MaRDI QIDQ4627855

No author found.

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/1505.06515

zbMATH Keywords

sum rulessummationzetacontour integrationzeroanalytic integrationmaster integration rule

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Singular functions, Cantor functions, functions with other special properties (26A30) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Other functions defined by series and integrals (33E20) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) One-variable calculus (26A06) Integral transforms, operational calculus (44A99)

Uses Software

• Maple
• Mathematica
• 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
• On an identity for zeros of Bessel functions
• NIST digital library of mathematical functions
• Master theorems for a family of integrals
• Series involving zeros of transcendental functions including zeta
• Further exploration of Riemann's functional equation
• Exploring Riemann’s functional equation
• On the exact location of the non-trivial zeros of Riemann's zeta function

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