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

Abstract

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

Cited by in corpus (3)

• The balanced Voronoi formulas for GL(n)
• An extension of the Bourgain-Sarnak-Ziegler theorem with modular applications
• Quadratic forms connected with Fourier coefficients of holomorphic and Maass cusp forms