Congruences modulo powers of 11 for some partition functions

Wang, Liuquan

doi:10.1090/proc/13858

Congruences modulo powers of 11 for some partition functions
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Proc. Amer. Math. Soc. 146 (2018), 1515-1528 Request permission

Abstract:

Let $R_{0}(N)$ be the Riemann surface of the congruence subgroup $\Gamma _{0}(N)$ of $\mathrm {SL}_{2}(\mathbb {Z})$. Using some properties of the field of meromorphic functions on $R_{0}(11)$, we confirm a conjecture of H.H. Chan and P.C. Toh [J. Number Theory 130 (2010), pp. 1898–1913] about the partition function $p(n)$. Moreover, we prove three infinite families of congruences modulo arbitrary powers of 11 for other partition functions, including 11-regular partitions and 11-core partitions.

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