Congruences for coefficients of modular functions in levels 3, 5, and 7\n with poles at 0

2020/01/10 by Paul Jenkins, Jenkins, Paul, Ryan Keck +1
Mathematics · #11F30 #11F37 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2001.04337

openalex publication_date 2020/01/10 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We give congruences modulo powers of p \∈ 3, 5,7 for the Fourier\ncoefficients of certain modular functions in level p with poles only at 0,\nanswering a question posed by Andersen and the first author and continuing work\ndone by the authors and Moss. The congruences involve a modulus that depends on\nthe base p expansion of the modular form's order of vanishing at \∞.\n

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