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Remarks on a formula of Ramanujan

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  06 February 2024

Andrés Chirre Open the ORCID record for Andrés Chirre [Opens in a new window]  and
Steven M. Gonek Open the ORCID record for Steven M. Gonek [Opens in a new window]
Andrés Chirre
Affiliation:
Departamento de Ciencias - Sección Matemáticas, Pontificia Universidad Católica del Perú, Lima, Peru (cchirre@pucp.edu.pe)
Steven M. Gonek
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627, USA (gonek@math.rochester.edu)
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Abstract

Assuming an averaged form of Mertens’ conjecture and that the ordinates of the non-trivial zeros of the Riemann zeta function are linearly independent over the rationals, we analyse the finer structure of the terms in a well-known formula of Ramanujan.

Keywords

Riemann zeta functionnontrivial zerosRiemann hypothesisMöbius μ function

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 155 , Issue 4 , August 2025 , pp. 1543 - 1554
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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