Central limit theorem for Hecke eigenvalues

TL;DR

This paper establishes a central limit theorem for Hecke eigenvalues associated with split simple algebraic groups over the rationals, using irreducible characters of compact Lie groups to generalize previous results.

Contribution

It introduces a general framework for the CLT of Hecke eigenvalues for a broad class of algebraic groups over , expanding the scope of prior specific cases.

Findings

Proves the CLT for Hecke eigenvalues in a general setting.

Utilizes irreducible characters of compact Lie groups in the proof.

Extends previous results to a wider class of algebraic groups.

Abstract

In this paper, we obtain the central limit theorem of Hecke eigenvalues in very general setting of split simple algebraic groups over $\mathbb{Q}$, using irreducible characters of compact Lie groups.