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A uniform asymptotic formula for the second moment of primitive \(L\)-functions on the critical line. (English. Russian original) Zbl 1397.11129

Proc. Steklov Inst. Math. 294, 13-46 (2016); translation from Tr. Mat. Inst. Steklova 294, 20-53 (2016).
The authors obtain an asymptotic formula for the second moment of a family of automorphic \(L\)-functions associated to primitive forms of even weight and prime power level. As an application, they estimate the error term uniformly in level, weight, shift, and twist.

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)

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References:

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