Kaneko, Ikuya (2022) Euler Product Asymptotics for Dirichlet L-Functions. Bulletin of the Australian Mathematical Society, 106 (1). pp. 48-56. ISSN 0004-9727. doi:10.1017/s0004972721001003. https://resolver.caltech.edu/CaltechAUTHORS:20220201-326205400
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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.
| Item Type: | Article | |||||||||
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| Additional Information: | © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc. Received 3 October 2021; accepted 25 October 2021; first published online 7 January 2022. The author acknowledges the support of the Masason Foundation and the Spirit of Ramanujan STEM Talent Initiative. This article is an outgrowth of the author’s collaborative work with Koyama [4] on Euler products of Selberg zeta functions in the critical strip. Special thanks are owed to Shin-ya Koyama and Nobushige Kurokawa for illuminating discussions. | |||||||||
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| Subject Keywords: | Dirichlet L-functions, partial Euler products, deep Riemann hypothesis | |||||||||
| Issue or Number: | 1 | |||||||||
| Classification Code: | 2020 Mathematics subject classification: primary 11M06; secondary 11M26 | |||||||||
| DOI: | 10.1017/s0004972721001003 | |||||||||
| Record Number: | CaltechAUTHORS:20220201-326205400 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20220201-326205400 | |||||||||
| Official Citation: | Kaneko, I. (2022). Euler Product Asymptotics for Dirichlet L-Functions. Bulletin of the Australian Mathematical Society, Bulletin of the Australian Mathematical Society, 106(1), 48-56. doi:10.1017/S0004972721001003 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 113205 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 01 Feb 2022 23:02 | |||||||||
| Last Modified: | 02 Aug 2022 19:23 |
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