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arXiv · 2408.09628

Congruences modulo powers of $5$ for odd ranks

Renrong Mao·Zhiqian Zhou
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Abstract

In 2007, Andrews studied the odd Durfee symbols and their odd ranks. Let $N^0(m,k,n)$ denote the number of odd Durfee symbols of $n$ with odd rank congruent to $m$ modulo $k$. Motivated by Andrews' work, many authors obtained generating functions of $N^0(m,k,n)$ from which relations between odd ranks are proved. In this paper, we establish a family of congruences for odd ranks modulo powers of $5$.

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Renrong Mao, Zhiqian Zhou. 2024-08-19. Congruences modulo powers of $5$ for odd ranks. https://arxiv.org/abs/2408.09628

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