Mean value theorems for the double zeta-function

Kohji Matsumoto; Hirofumi Tsumura

doi:10.2969/jmsj/06710383

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Mean value theorems for the double zeta-function

Kohji Matsumoto, Hirofumi Tsumura

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

JOURNAL FREE ACCESS

2015 Volume 67 Issue 1 Pages 383-406

DOI https://doi.org/10.2969/jmsj/06710383

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Abstract

We prove asymptotic formulas for mean square values of the Euler double zeta-function ζ₂(s₀,s), with respect to ℑs. Those formulas enable us to propose a double analogue of the Lindelöf hypothesis.

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