Distribution of Hecke eigenvalues in large arithmetic progressions (Yongxiao Lin, EPFL Lausanne)Séminaire « Arithmétique »
M2 Kampé de Fériet
Let $\lambda_F(n)$ be the Hecke eigenvalues of a $GL_d$ automorphic form $F$. One question in number theory is the distribution of $\lambda_F(n)$, $n \geq 1$ when they are restricted to arithmetic progressions modulo large q. We will discuss the level of distribution problem for the sequence $\lambda_F(n)$, $n \geq 1$ and present cases where factorisation of the coefficients $\lambda_F(n)$ or the moduli q allows one to passing the trivial exponent of distribution. We will explain how this is related to the study of sums of $\lambda_F(n)$ weighted by a trace function K modulo q. This talk is based on joint works with E. Kowalski, Ph. Michel, and W. Sawin.