Central limit theorem for Hecke eigenvalues

Key Points

• 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.