398 research outputs found
Vanishing and Non-Vanishing Dirichlet Twists of L-Functions of Elliptic Curves
Let L(E/Q,s) be the L-function of an elliptic curve E defined over the
rational field Q. We examine the vanishing and non-vanishing of the central
values L(E,1,\chi) of the twisted L-function as \chi ranges over Dirichlet
characters of given order.Comment: To appear in Journal of the London Mathematical Societ
Simultaneous nonvanishing of Dirichlet -functions and twists of Hecke-Maass L-functions
We prove that given a Hecke-Maass form for and
a sufficiently large prime , there exists a primitive Dirichlet character
of conductor such that the -values and do not vanish. We expect the same method to
work for any large integer
Mean values with cubic characters
We investigate various mean value problems involving order three primitive
Dirichlet characters. In particular, we obtain an asymptotic formula for the
first moment of central values of the Dirichlet L-functions associated to this
family, with a power saving in the error term. We also obtain a large-sieve
type result for order three (and six) Dirichlet characters.Comment: 22 pages; greatly shortened, simplified and corrected versio
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