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arXiv · 1204.2253

Averages of twisted L-functions

Julia Jackson·Andrew Knightly
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Abstract

We use a relative trace formula on GL(2) to compute a sum of twisted modular L-functions anywhere in the critical strip, weighted by a Fourier coefficient and a Hecke eigenvalue. When the weight k or level N is sufficiently large, the sum is nonzero. Specializing to the central point, we show in some cases that the resulting bound for the average is as good as that predicted by the Lindelof hypothesis in the k and N aspects.

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Julia Jackson, Andrew Knightly. 2012-04-10. Averages of twisted L-functions. https://doi.org/10.1017/s1446788715000142

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