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SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN $L$-FUNCTIONS

Part of: Zeta and $L$-functions: analytic theory Algebraic number theory: global fields

Published online by Cambridge University Press:  13 August 2019

ARUL SHANKAR ,
ANDERS SÖDERGREN  and
NICOLAS TEMPLIER
ARUL SHANKAR
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada; arul.shnkr@gmail.com
ANDERS SÖDERGREN
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden; andesod@chalmers.se
NICOLAS TEMPLIER
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA; templier@math.cornell.edu

Abstract

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We study various families of Artin $L$-functions attached to geometric parametrizations of number fields. In each case we find the Sato–Tate measure of the family and determine the symmetry type of the distribution of the low-lying zeros.

MSC classification

Primary: 11R42: Zeta functions and $L$-functions of number fields 11M41: Other Dirichlet series and zeta functions
Secondary: 11M50: Relations with random matrices
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e23
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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