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This is a Quantitative Study study.

October 12, 2025Open Access

A maple package for modular function and its application to partition functions

Key Points

The Maple package reveals new partition congruences, enhancing our understanding of modular forms.
Key findings include the discovery of new partition congruences and their proofs based on Ramanujan-Kolberg identities.
This work employs Radu's algorithm and other modular form tools to manipulate q-series and establish important congruences.
The significance of this research indicates broader implications for combinatorial mathematics and modular function theory.

Abstract

Abstract A Maple package, which includes Radu’s algorithm and other algorithms of modular form tools, is provided. This enables us to prove or discover congruences for some restricted partition functions through building up Ramanujan-Kolberg identities, as well as perform many manipulations related to q-series and modular forms, such as dissection formulas and the Hecke operator. A pair of new partition congruences and their proof were found by this program as examples.

A maple package for modular function and its application to partition functions

Key Points

Abstract

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