Journal of the Mathematical Society of Japan

Mean value theorems for the double zeta-function

Kohji MATSUMOTO and Hirofumi TSUMURA

Full-text: Open access

Abstract

We prove asymptotic formulas for mean square values of the Euler double zeta-function $\zeta_2(s_0,s)$, with respect to $\Im s$. Those formulas enable us to propose a double analogue of the Lindelöf hypothesis.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 1 (2015), 383-406.

Dates
First available in Project Euclid: 22 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1421936557

Digital Object Identifier
doi:10.2969/jmsj/06710383

Mathematical Reviews number (MathSciNet)
MR3304026

Zentralblatt MATH identifier
1355.11088

Subjects
Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Keywords
double zeta-functions mean values Lindelöf hypothesis Euler's constant

Citation

MATSUMOTO, Kohji; TSUMURA, Hirofumi. Mean value theorems for the double zeta-function. J. Math. Soc. Japan 67 (2015), no. 1, 383--406. doi:10.2969/jmsj/06710383. https://projecteuclid.org/euclid.jmsj/1421936557


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