Fourier coefficients of symmetric power L-functions

Hengcai Tang (1) , Jie Wu (2)

1 Henan University
2 IECL - Institut Élie Cartan de Lorraine

Let f be a Hecke eigencusp form of even integral weight k or Maass cusp form for the full modular group SL 2 (Z). Denote by λ sym m f (n) the nth normalized coefficient of the Dirichlet expansion of the mth symmetric power L-function associated to f. In this paper, we establish some bounds for nx λ sym m f (n), nx λ f (n m), which improve the corresponding results of Lau & Lü [9].

Domaines: Théorie des nombres [math.NT]

Hengcai Tang, Jie Wu. Fourier coefficients of symmetric power L-functions. Journal of Number Theory, 2016, 167, pp.147-160. ⟨10.1016/j.jnt.2016.03.005⟩. ⟨hal-01313347⟩