The second moment of Dirichlet twists of Hecke L-functions

 

 

State

 

Submitted on December 15, 2008.

Accepted for publication on January 26, 2009.

Published in Acta Arithmetica 140, 57--65 (2009).

 

Abstract

 

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 Stefanickiís 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.

 

 

twisted.pdf

 

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