Nonlinear twists and moments of $L$-functions

Let $F$ belong to the extended Selberg class $\mathcal S^\sharp $. We show how a suitable hypothesis on the analytic continuation of a certain nonlinear twist of $F^2$, namely the self-reciprocal twist, implies a sharp bound for the mean-square of $F(1/2+it)$.

Published in Open Access (under CC-BY license).