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Mean square formula for the double zeta-function. (English) Zbl 1407.11107
Summary: We prove the mean square formula of the Euler-Zagier type double zeta-function \(\zeta_{2}(s_{1},s_{2})\) and provide an improvement on the \(\Omega\) results of [the first author et al., Indag. Math., New Ser. 21, No. 1–2, 16–29 (2011; Zbl 1253.11084)]. We also calculate the double integral \(\int_{2}^{N}\int_{2}^{T}|\zeta_{2}(s_{1},s_{2})|^{2}dt_{1} dt_{2}\) under certain conditions.

11M41 Other Dirichlet series and zeta functions
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
Zbl 1253.11084
Full Text: DOI Euclid
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