Moments of fourier coefficients of symmetric power representations with applications

Venue: Room 200-9, Sir Shaw Run Run Business Administration building, School of Mathematical Sciences, Yuquan Campus 

Speaker: Dr. Liyang Yang, Department of Mathematics, California Institute of Technology

Abstract: In this talk, we give nontrivial upper bounds for certain moments of Fourier coefficients associated to $\Sym^k\pi,$ where $\pi$ is a non-dihedral cuspidal representation of $\GL(2,\mathbb{A}_{\mathbb{Q}})$ and $1\leq k \leq 3.$ These bounds generalize known results in holomorphic case to Maass forms, without assuming Ramanujan-Petersson conjecture. Also, some applications will be discussed.