Yuk-Kam Lau, Université Henri Poincaré, Nancy et Université de Hong-Kong

Summatory functions involving the Fourier coefficients of primitive cusp forms

Let t_φ(n) denote the nth normalized Fourier coefficient of a primitive holomorphic or
Maass cusp form φ for the full modular group. Our goal is to study the high moments
Σ_n≤x t_φ(n)^j and the mean value Σ_n≤x t_φ(n^j) over jth powers, through the (conjectural)
analytic properties of symmetric power L-functions.