2023/12/07 by Mingkuan Zhang, Yichao Zhang, Zhang, Mingkuan +1
Mathematics · #11F30 #11F41 #11F60 #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.2312.04169
openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that if ν has small norm with respect to the level and the weight, the ν-th Hilbert Poincaré series does not vanish identically. We also prove Selberg's identity on Kloosterman sums in the case of number fields, which implies certain vanishing and non-vanishing relations of Hilbert Poincaré series when the narrow class number is 1. Finally, we pass to the adelic setting and interpret the problem via Hecke operators.