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arXiv · 2303.05268

Andrews-Beck type congrences modulo powers of 5

Nankun Hong·Renrong Mao
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Abstract

Let $NT(m, k, n)$ denote the total number of parts in the partitions of n with rank congruent to m modulo k. Andrews proved Beck's conjecture on congruences for $NT(m, k, n)$ modulo 5 and 7. Generalizing Andrews'results, Chern obtain congruences for $NT(m, k, n)$ modulo 11 and 13. More recently, the second author use the theory of Hecke operators to establish congruences for such partition statistics modulo powers of primes $\ell \ge 7$. In this paper, we obtain Andrews-Beck type congruences modulo powers of 5.

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Nankun Hong, Renrong Mao. 2023-03-09. Andrews-Beck type congrences modulo powers of 5. https://arxiv.org/abs/2303.05268

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