Generation of cyclotomic Hecke fields by L-values of cusp forms on GL(2) with certain ℤ_p twist

2024/06/13 by Jaesung Kwon, Kwon, Jaesung
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2406.08939

openalex publication_date 2024/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let F be a number field, f an algebraic automorphic newform on GL(2) over F, p an odd prime does not divide the class number of F and the level of f. We prove that f is determined by its L-values twisted by Galois characters ϕ of certain ℤ_p-extension of F. Furthermore, if F is totally real or CM, then under some mild assumption on f, the compositum of the Hecke field of f and the cyclotomic field ℚ(ϕ) is generated by the algebraic L-values of f twisted by Galois characters ϕ of certain ℤ_p-extension of F.

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