The central limit theorem illustrates the statistical behaviors of Hecke eigenvalues under certain conditions.
In this framework, we focus on split simple algebraic groups, revealing complex interactions with representation.
Using irreducible characters of compact Lie groups, the theorem establishes foundational results in algebraic contexts.
This work has implications for understanding representation theory in number theory and algebraic geometry.
Abstract
Abstract In this paper, we obtain the central limit theorem of Hecke eigenvalues in the very general setting of split simple algebraic groups over ℚ, using irreducible characters of compact Lie groups.