Abstract
The moments of pure imaginary and integer orders of the function L(1, χ8p), where χ8p(n) = (8p/n) and p runs over all primes p > 2, are computed.In order to derive uniform variants of the theorems on moments, the extended Riemann hypothesis for the Dirichlet L-series must be used. As corollaries, the limiting distribution of the values of log L(1, χ8p) is studied, and quantitative analogs of the Ω-results for L(1, χ8p) are obtained. Previously, Ω-results for L(1, χ8p) were proved by Bateman, Chowla, and Erdos (1949–1950) and by Barban (1966), and their methods can easily be transferred to L(1, χ8p). Bibliography: 27 titles.
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