Central limit theorem for Hecke eigenvalues

Q: What type of study is this?

This is a Quantitative Study study.

Henry H. Kim; Satoshi Wakatsuki; Takuya Yamauchi

doi:10.1515/forum-2025-0044

September 11, 2025Forum Mathematicum

Central limit theorem for Hecke eigenvalues

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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.

Implication

Theorem shows central limit behavior of Hecke eigenvalues in algebraic groups, suggesting new insights in representation theory.

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.

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Cite This Study

Kim et al. (2025) studied this question.

synapsesocial.com/papers/68d463e931b076d99fa63323 https://doi.org/10.1515/forum-2025-0044

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Central limit theorem for Hecke eigenvalues

Key Points

Implication

Abstract

Discussion

Cite This Study

Central limit theorem for Hecke eigenvalues

Key Points

Implication

Abstract

Discussion

Cite This Study

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