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arXiv · 0812.2606

The second moment of Dirichlet twists of Hecke $L$-functions

Peng Gao·Rizwanur Khan·Guillaume Ricotta
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Abstract

Fix a Hecke cusp form $f$, and consider the $L$-function of $f$ twisted by a primitive Dirichlet character. As we range over all primitive characters of a large modulus $q$, what is the average behavior of the square of the central value of this $L$-function? Stefanicki proved an asymptotic valid only for $q$ having very few prime factors, and we extend this to almost all $q$.

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Peng Gao, Rizwanur Khan, Guillaume Ricotta. 2009-03-26. The second moment of Dirichlet twists of Hecke $L$-functions. https://doi.org/10.4064/aa140-1-4

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