Let $F$ belong to the extended Selberg class $\S^\sharp$. In this paper 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 $F(1/2+it)$.
Nonlinear twists and moments of L-functions
A. Perelli
2024-01-01
Abstract
Let $F$ belong to the extended Selberg class $\S^\sharp$. In this paper 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 $F(1/2+it)$.
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