Distribution of Hecke eigenvalues of newforms in short intervals

Jie Wu (1) , Wenguang Zhai (2)

1 IECL - Institut Élie Cartan de Lorraine
2 CUMT - China University of Mining and Technology

We explore nonvanishing of Hecke eigenvalues in short arithmetic progressions and their signs in short intervals by further developing B-free number method and studying moments in short intervals. We improve some results of Alkan & Zaharescu [3] and Lau & Wu [20] on the distribution of Hecke eigenvalues.

Domaines: Théorie des nombres [math.NT]

Jie Wu, Wenguang Zhai. Distribution of Hecke eigenvalues of newforms in short intervals. Quarterly Journal of Mathematics, 2013, 64 (2), pp.619-644. ⟨10.1093/qmath/has007⟩. ⟨hal-01278937⟩