The second
moment of Dirichlet twists of Hecke
L-functions
Submitted
on December 15, 2008.
Accepted
for publication on January 26, 2009.
Published in Acta Arithmetica 140, 57--65 (2009).
f
is a fixed holomorphic cusp of level 1.
Purpose:
To study the asymptotic behaviour of the
second moment of the twisted L-function of f by the primitive characters of
conductor q as q goes to infinity.
Result:
We
get an asymptotic formula for the second moment of the twisted L-function of f
by the primitive characters of conductor q with a polynomial saving in the
error term and as q generically goes to infinity. This is a substancial
improvement over Stefanicki’s previous result since
his result holds for almost no q. It should be seen as an analogue of the
fourth moment of Dirichlet L-functions.
The previous texts are
not the published one. For they should not be quoted.
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