Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces

研究成果: ジャーナルへの寄稿記事

2 引用 (Scopus)

抄録

We present an example of the Selberg type zeta function for non-compact higher rank locally symmetric spaces. This is a generalization of Selberg's unpublished work [26] to non-compact cases. We study certain Selberg type zeta functions and Ruelle type zeta functions attached to the Hilbert modular group of a real quadratic field. We show that they have meromorphic extensions to the whole complex plane and satisfy functional equations. The method is based on considering the differences among several Selberg trace formulas with different weights for the Hilbert modular group. Besides as an application of the differences of the Selberg trace formula, we also obtain an asymptotic average of the class numbers of indefinite binary quadratic forms over the real quadratic integer ring.

元の言語英語
ページ(範囲)396-453
ページ数58
ジャーナルJournal of Number Theory
147
DOI
出版物ステータス出版済み - 2 1 2015

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Selberg Trace Formula
Riemann zeta function
Hilbert
Modular Group
Binary Quadratic Forms
Locally Symmetric Spaces
Real Quadratic Fields
Class number
Meromorphic
Argand diagram
Functional equation
Ring
Integer

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

これを引用

Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces. / Gon, Yasuro.

:: Journal of Number Theory, 巻 147, 01.02.2015, p. 396-453.

研究成果: ジャーナルへの寄稿記事

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