Algebraicity of critical Hecke L-values

2025/11/07 by Kings, Guido, Sprang, Johannes
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.05198

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

In this survey, we review the known results on the algebraicity of critical values of Hecke L-functions and explain the new developments in \citeKings-Sprang.

Citations

• Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation
• Katz type p-adic L-functions for primes p non-split in the CM field
• Algebraic theta functions and Eisenstein-Kronecker numbers
• p-adic Fourier Theory

Related

• On Deligne's conjecture for Hecke characters
• Notes on the arithmetic of Hecke L-functions
• Deligne's conjecture on the critical values of Hecke L-functions
• An explicit formula for Hecke L-functions
• Uniform Bound for Hecke L-Functions