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A NOTE ON THE ZEROS OF L-FUNCTIONS ASSOCIATED TO FIXED-ORDER DIRICHLET CHARACTERS

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

Published online by Cambridge University Press:  18 December 2023

C. C. CORRIGAN
C. C. CORRIGAN*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
*
e-mail: c.corrigan@student.unsw.edu.au
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Abstract

We use the Weyl bound for Dirichlet L-functions to derive zero-density estimates for L-functions associated to families of fixed-order Dirichlet characters. The results improve on previous bounds given by the author when $\sigma $ is sufficiently distant from the critical line.

Keywords

Dirichlet charactersDirichlet L-functionszero-density estimates

MSC classification

Primary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses
Secondary: 11N35: Sieves
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 10
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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