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EULER PRODUCT ASYMPTOTICS FOR DIRICHLET $\boldsymbol {L}$-FUNCTIONS

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

Published online by Cambridge University Press:  07 January 2022

IKUYA KANEKO Open the ORCID record for IKUYA KANEKO [Opens in a new window]
IKUYA KANEKO*
Affiliation:
Department of Mathematics, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
*
e-mail: [email protected]
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Abstract

The aim of this article is to establish the behaviour of partial Euler products for Dirichlet L-functions under the generalised Riemann hypothesis (GRH) via Ramanujan’s work. To understand the behaviour of Euler products on the critical line, we invoke the deep Riemann hypothesis (DRH). This work clarifies the relation between GRH and DRH.

Keywords

Dirichlet L-functionspartial Euler productsdeep Riemann hypothesis

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
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 1 , August 2022 , pp. 48 - 56
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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