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I'm looking for a reference for some questions related to the moments of Dirichlet characters on the critical line, $$ M_k(T;\chi) = \int_T^{2T} |L(1/2+it,\chi)|^{2k}\,dt, $$ where $\chi$ is a ...

I'd like to know why it is important to know the moments of the derivatives of $L$-functions. The moments of $L$-functions are related to the Lindelöf Hypothesis, but what about the moments of the ...