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

ARUL SHANKAR; ANDERS SÖDERGREN; NICOLAS TEMPLIER

doi:10.1017/fms.2019.18

Forum of Mathematics, Sigma (Jan 2019)

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

ARUL SHANKAR,
ANDERS SÖDERGREN,
NICOLAS TEMPLIER

Affiliations

ARUL SHANKAR: Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada;
ANDERS SÖDERGREN: Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden;
NICOLAS TEMPLIER: Department of Mathematics, Cornell University, Ithaca, NY 14853, USA;

DOI: https://doi.org/10.1017/fms.2019.18
Journal volume & issue: Vol. 7

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.

Published in Forum of Mathematics, Sigma

ISSN: 2050-5094 (Online)
Publisher: Cambridge University Press
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma

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