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Mean value theorems for the double zeta-function

Number Theory 2016-04-29 v5
Authors: Kohji Matsumoto , Hirofumi Tsumura
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Abstract

We prove asymptotic formulas for mean square values of the Euler double zeta-function ζ2(s0,s)\zeta_2(s_0,s), with respect to ℑs\Im s. Those formulas enable us to propose a double analogue of the Lindel{\"o}f hypothesis.

Keywords

riemann zeta function zeta values and euler sums zeta functions

Cite

@article{arxiv.1203.2242,
  title  = {Mean value theorems for the double zeta-function},
  author = {Kohji Matsumoto and Hirofumi Tsumura},
  journal= {arXiv preprint arXiv:1203.2242},
  year   = {2016}
}

Comments

23 pages

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R2 v1 2026-06-21T20:32:05.710Z