Averages of values of 𝐿-series

Alkan, Emre

doi:10.1090/S0002-9939-2012-11506-0

Averages of values of $L$-series
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Proc. Amer. Math. Soc. 141 (2013), 1161-1175 Request permission

Abstract:

We obtain an exact formula for the average of values of $L$-series over two independent odd characters. The average of any positive moment of values at $s=1$ is then expressed in terms of finite cotangent sums subject to congruence conditions. As consequences, bounds on such cotangent sums, limit points for the average of first moment of $L$-series at $s=1$ and the average size of positive moments of character sums related to the class number are deduced.

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