Year: 2026
Type: preprint
Abstract: We introduce a systematic framework for constructing holonomic recurrences from meromorphic modular forms. Its central ingredient is a modular analogue of creative telescoping, which turns finite-dimensional quotients of spaces of meromorphic modular forms into explicit recurrence operators. This provides a common explanation for several previously isolated examples: it recovers Apéry's recurrence, Beukers' modular constructions and Zagier's seven sporadic recurrences. The framework also produces a large collection of new examples across different weights and groups. The modular origin of these sequences also confers them with non-trivial arithmetic properties, such as denominator bounds, irrationality statements, and $p$-adic congruences.
Source: arXiv (Cornell University)
Author: Au, Kam Cheong
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221786509