The Shintani double zeta functions-Reference-Cited by-同舟云学术

The Shintani double zeta functions

Published:2022-03-01 Issue:2 Volume:34 Page:469-505
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Kim Henry H.¹,Tsuzuki Masao²,Wakatsuki Satoshi³

Affiliation:

1. Department of Mathematics , University of Toronto , Toronto , Ontario M5S 2E4, Canada ; and Korea Institute for Advanced Study, Seoul, Korea

2. Department of Science and Technology , Sophia University , Kioi-cho 7-1 Chiyoda-ku Tokyo , Japan

3. Faculty of Mathematics and Physics , Institute of Science and Engineering , Kanazawa University , Kakumamachi , Kanazawa , Ishikawa, 920-1192 , Japan

Abstract

Abstract In this paper, we give an explicit formula for the Shintani double zeta functions with any ramification in the most general setting of adeles over an arbitrary number field. Three applications of the explicit formula are given. First, we obtain a functional equation satisfied by the Shintani double zeta functions in addition to Shintani’s functional equations. Second, we establish the holomorphicity of a certain Dirichlet series generalizing a result by Ibukiyama and Saito. This Dirichlet series occurs in the study of unipotent contributions of the geometric side of the Arthur–Selberg trace formula of the symplectic group. Third, we prove an asymptotic formula of the weighted average of the central values of quadratic Dirichlet L-functions.

Funder

Natural Sciences and Engineering Research Council of Canada

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2020-0251/pdf

Reference31 articles.

1. V. Blomer, Subconvexity for a double Dirichlet series, Compos. Math. 147 (2011), no. 2, 355–374.

2. B. Brubaker, D. Bump, G. Chinta, S. Friedberg and J. Hoffstein, Weyl group multiple Dirichlet series. I, Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory, Proc. Sympos. Pure Math. 75, American Mathematical Society, Providence (2006), 91–114.

3. D. Bump, S. Friedberg and J. Hoffstein, Sums of twisted GL⁢(3){{\rm GL}(3)} automorphic L-functions, Contributions to Automorphic Forms, Geometry, and Number Theory, Johns Hopkins University, Baltimore (2004), 131–162.

4. G. Chinta and P. E. Gunnells, Constructing Weyl group multiple Dirichlet series, J. Amer. Math. Soc. 23 (2010), no. 1, 189–215.

5. H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217 (1975), no. 3, 271–285.

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