Abstract
Assuming the generalized Riemann hypothesis, we prove upper bounds for moments of arbitrary products of automorphic L-functions and for Dedekind zeta-functions of Galois number fields on the critical line. As an application, we use these bounds to estimate the variance of the coefficients of these zeta- and L-functions in short intervals. We also prove upper bounds for moments of products of central values of automorphic L-functions twisted by quadratic Dirichlet characters and averaged over fundamental discriminants.
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