Absolute zeta functions and absolute automorphic forms

被引：9

作者：

Kurokawa, Nobushige ^{[1
]}

Tanaka, Hidekazu ^{[2
]}

机构：

[1] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan

[2] Shibaura Inst Technol, Dept Math, Fukasaku, Saitama 3378570, Japan

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2018年 / 126卷

关键词：

Zeta function; Automorphic form; Euler constant; Transcendency; F-1;

D O I：

10.1016/j.geomphys.2018.01.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct absolute zeta functions from absolute automorphic forms via the zeta regularization. We study analytic properties of absolute zeta functions. Especially we look at regularized Euler constants. We show a generalization of Euler's formula for the original Euler constant by using special values of absolute zeta functions. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：168 / 180

页数：13

共 18 条

[1]

Baker A., 1975, TRANSCENDENTAL NUMBE

[2]

Barnes E. W., 1904, T CAMB PHILOS SOC, V19, P374

[3]

Connes A., 2011, Noncommutative geometry, arithmetic, and related topics, P75

[4] Schemes over F1 and zeta functions [J].

Connes, Alain ;

Consani, Caterina .

COMPOSITIO MATHEMATICA, 2010, 146 (06) :1383-1415

[5]

Deitmar A, 2006, P JPN ACAD A-MATH, V82, P141

[6]

Deitmar A, 2015, ABH MATH SEM HAMBURG, V85, P59, DOI 10.1007/s12188-015-0104-3

[7] LOCAL L-FACTORS OF MOTIVES AND REGULARIZED DETERMINANTS [J].

DENINGER, C .

INVENTIONES MATHEMATICAE, 1992, 107 (01) :135-150

[8]

Euler L., 1775, NOVI COMENTARII ACAD, V19, P66

[9]

Euler L, 1780, NOVA ACTA ACAD SCI I, V1777, P29

[10]

Euler L, 1776, NOVI COMMENT ACAD SC, V20, P59

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