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

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

2008-12-14

arxiv.org/abs/0812.2606v2

Mathematics

Number Theory

9 pages

Scientific paper

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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