On the modularity of solutions of certain differential equations of\n hypergeometric type

2021/06/21 by Hicham Saber, Saber, Hicham, Abdellah Sebbar +1
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2106.10842

openalex publication_date 2021/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to provide answers to some questions raised in a\npaper by Kaneko and Koike about the modularity of the solutions of a\ndifferential equations of hypergeometric type. In particular, we provide a\nnumber-theoretic explanation of why the modularity of the solutions occurs in\nsome cases and does not occur in other cases. This also proves their conjecture\non the completeness of the list of modular solutions after adding some missing\ncases.\n

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