Coefficient Bounds for Level 2 Cusp Forms and Modular Functions

2014/08/05 by Paul A. Jenkins, Paul Jenkins, Kyle Pratt +2
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1408.1083

arxiv created 2014/08/05 · openalex publication_date 2014/08/05 · arxiv updated 2014/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give explicit upper bounds for the coefficients of arbitrary weight k, level 2 cusp forms, making Deligne's well-known O(n^(k-1)/(2)+ε) bound precise. We also derive asymptotic formulas and explicit upper bounds for the coefficients of certain level 2 modular functions.

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