Asymptotics and sign patterns of Hecke polynomial coefficients

2024/10/15 by Erick Ross, Hui Xue, Ross, Erick +1 · 1 citation
Physics and Astronomy · #11F11 (Secondary) #11F25 (Primary) 11F72 #FOS: Mathematics #Number Theory (math.NT) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2410.12008

openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the asymptotic behavior of the coefficients of Hecke polynomials. In particular, this allows us to determine signs of these coefficients when the level or the weight is sufficiently large. In all but finitely many cases, this also verifies a conjecture on the nanvanishing of the coefficients of Hecke polynomials.

Cited by

• Dimension sequences of modular forms

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