Moments of quadratic Dirichlet character sums
Abstract
We consider moments of higher powers of quadratic Dirichlet character sums. In a restricted region, we give their asymptotic behavior by using de la Bret\`eche's multivariable Tauberian theorem. We also give the lower bound of the exponent of factor in the conjecture of Jutila. As an application, we give a lower bound of a weighted average of shifted moments of quadratic Dirichlet L-functions.
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