A simple proof of the Atkin-O'Brien partition congruence conjecture for powers of 13

Frank Garvan; Zhumagali Shomanov

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arXiv · 2504.10824

A simple proof of the Atkin-O'Brien partition congruence conjecture for powers of 13

Frank Garvan·Zhumagali Shomanov

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Abstract

In 1967, Atkin and O'Brien conjectured congruences for the partition function involving Hecke operators modulo powers of 13. In this paper, we provide a simple proof of this conjecture.

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Frank Garvan, Zhumagali Shomanov. 2025-04-15. A simple proof of the Atkin-O'Brien partition congruence conjecture for powers of 13. https://arxiv.org/abs/2504.10824

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