Nonlinear twists and moments of $L$-functions
Volume 214 / 2024
Acta Arithmetica 214 (2024), 153-171
MSC: Primary 11M41; Secondary 11M26
DOI: 10.4064/aa230329-3-6
Published online: 27 March 2024
Abstract
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 $F(1/2+it)$.
