Strong orthogonality between the Möbius function, additive characters and Fourier coefficients of cusp forms

Abstract

AbstractLet$\nu _{f}(n)$be the$n\mathrm{th}$normalized Fourier coefficient of a Hecke–Maass cusp form$f$for${\rm SL }(2,\mathbb{Z})$and let$\alpha $be a real number. We prove strong oscillations of the argument of$\nu _{f}(n)\mu (n) \exp (2\pi i n \alpha )$as$n$takes consecutive integral values.