Power sums of Hecke's eigenvalues and application

Jie Wu (1)

1 IECN - Institut Élie Cartan de Nancy

We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi's recent results on higher order symmetric powers. As an application, we improve Kohnen, Lau & Shparlinski's lower bound for the number of Hecke eigenvalues of same signs.

Domaines: Théorie des nombres [math.NT]

Jie Wu. Power sums of Hecke's eigenvalues and application. 2008. ⟨hal-00291672⟩