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arXiv · 1404.7845

The second moment of twisted modular L-functions

Valentin Blomer·Djordje Milićević
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Abstract

We prove an asymptotic formula with a power saving error term for the (pure or mixed) second moment of central values of L-functions of any two (possibly equal) fixed cusp forms f, g twisted by all primitive characters modulo q, valid for all sufficiently factorable q including 99.9% of all admissible moduli. The two key ingredients are a careful spectral analysis of a potentially highly unbalanced shifted convolution problem in Hecke eigenvalues and power-saving bounds for sums of products of Kloosterman sums where the length of the sum is below the square-root threshold of the modulus. Applications are given to simultaneous non-vanishing and lower bounds on higher moments of twisted L-functions.

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Valentin Blomer, Djordje Milićević. 2014-04-30. The second moment of twisted modular L-functions. https://doi.org/10.1007/s00039-015-0318-7

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