On the expected result for the second moment of twisted L -functions





Published in Mathematisches Forschungsinstitut Oberwolfach, Report No. 33/2009, Explicit Methods in Number Theory (July 12th-July 22nd), 14--16 (2009).




Finding an asymptotic formula for the fourth moment of Dirichlet L-functions with a power saving in the error term should be philosophically as difficult as the corresponding question for the second moment of twisted L-functions. It turns out that the first problem has been completely solved by M. Young in the prime modulus case whereas the best result for the second one is only an asymptotic formula with a logarithmic saving in the error term so far. The purpose of this note is to identify the underlying analytic issue, which occurs in the second question.






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