The number of Hecke eigenvalues of same signs

Yuk Kam Lau (1) , Jie Wu (2)

1 Department of Mathematics
2 IECN - Institut Élie Cartan de Nancy

We give the best possible lower bounds in order of magnitude for the number of positive and negative Hecke eigenvalues. This improves upon a recent work of Kohnen, Lau & Shparlinski. Also, we study an analogous problem for short intervals.

Mots clés: Fourier coefficients of modular forms; B-free numbers

Domaines: Théorie des nombres [math.NT]

Yuk Kam Lau, Jie Wu. The number of Hecke eigenvalues of same signs. 2008. ⟨hal-00347529⟩