Computations on Overconvergence Rates Related to the Eisenstein Family

2023/06/20 by Bryan Advocaat, Advocaat, Bryan
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.11537

openalex publication_date 2023/06/20 · openalex created_date 2023/06/22 · openalex updated_date 2026/07/28

Abstract

We provide for primes p≥ 5 a method to compute valuations appearing in the "formal" Katz expansion of the family \fracE_k^∗V(E_k^∗) derived from the family of Eisenstein series E_k^∗. The overconvergence rates of the members of this family go back to a conjecture from Coleman. We will describe two algorithms: the first one to compute the Katz expansion of an overconvergent modular form and the second one, which uses the first algorithm, to compute valuations appearing in the "formal" Katz expansion. Based on data obtained using these algorithms we make a precise conjecture about a constant appearing in the overconvergence rates related to the classical Eisenstein series at level p.

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