Mean value theorems for the double zeta-function

被引：12

作者：

Matsumoto, Kohji ^{[1
]}

Tsumura, Hirofumi ^{[2
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Tokyo 1920397, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2015年 / 67卷 / 01期

关键词：

double zeta-functions; mean values; Lindelof hypothesis; Euler's constant; ANALYTIC CONTINUATION; EQUATIONS;

D O I：

10.2969/jmsj/06710383

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove asymptotic formulas for mean square values of the Euler double zeta-function zeta(2)(s(0), s), with respect to is. Those formulas enable us to propose a double analogue of the Lindelof hypothesis.

引用

页码：383 / 406

页数：24

共 14 条

[1] Analytic continuation of multiple zeta-functions and their values at non-positive integers [J].

Akiyama, S ;

Egami, S ;

Tanigawa, Y .

ACTA ARITHMETICA, 2001, 98 (02) :107-116

[2] Multiple zeta values, poly-Bernoulli numbers, and related zeta functions [J].

Arakawa, T ;

Kaneko, M .

NAGOYA MATHEMATICAL JOURNAL, 1999, 153 :189-209

[3] THE MEAN-VALUE OF THE RIEMANN ZETA-FUNCTION [J].

ATKINSON, FV .

ACTA MATHEMATICA, 1949, 81 (04) :353-376

[4] EXPLICIT EVALUATION OF EULER SUMS [J].

BORWEIN, D ;

BORWEIN, JM ;

GIRGENSOHN, R .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1995, 38 :277-294

[5] On the estimation of the order of Euler-Zagier multiple zeta-functions [J].

Ishikawa, H ;

Matsumoto, K .

ILLINOIS JOURNAL OF MATHEMATICS, 2003, 47 (04) :1151-1166

[6] Analytic properties of double zeta-functions [J].

Kiuchi, I. ;

Tanigawa, Y. ;

Zhai, W. .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2011, 21 (1-2) :16-29

[7]

Kiuchi I, 2006, ANN SCUOLA NORM-SCI, V5, P445

[8]

Komori Y, 2010, PUBL MATH-DEBRECEN, V77, P15

[9] Functional equations for double zeta-functions [J].

Matsumoto, K .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2004, 136 :1-7

[10] Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series [J].

Matsumoto, K .

NAGOYA MATHEMATICAL JOURNAL, 2003, 172 :59-102

← 1 2 →