Special values of<i>L</i>-functions of one-motives over function fields-Reference-Cited by-同舟云学术

Special values ofL-functions of one-motives over function fields

Published:2022-11-23 Issue:793 Volume:2022 Page:281-304
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Geisser Thomas H.¹^ORCID,Suzuki Takashi²

Affiliation:

1. Rikkyo University , Ikebukuro , Tokyo , Japan

2. Chuo University , Kasuga , Tokyo , Japan

Abstract

AbstractThe purpose of this paper is to give a formula for the leading coefficient ats=1

{s=1}

of theL-function of one-motives over function fields in terms of Weil-étale cohomology, generalizing the Weil-étale version of the Birch and Swinnerton-Dyer conjecture in the authors’ previous work. As a consequence we express the Tamagawa number of a torus introduced by Ono–Oesterlé in terms of Weil-étale cohomology, and reprove their Tamagawa number formula.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0081/pdf

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