Abstract
In this note, we prove an asymptotic formula for the mean-square of the so-called periodic zeta-function with respect to the parameter. This may be compared with similar formulae for Dirichlet L-functions to (multiplicative) residue class characters due to Paley and others. The periodic zeta-function is the twist of the Riemann zeta-function with an additive character.
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Tongsomporn, J., Steuding, J. Discrete Moments of Additive Twists. I: The Mean-Square. Lith Math J 59, 412–424 (2019). https://doi.org/10.1007/s10986-019-09450-z
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DOI: https://doi.org/10.1007/s10986-019-09450-z