Congruences modulo powers of 11 for some partition functions
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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.References
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Additional Information
- Liuquan Wang
- Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, People’s Republic of China — and — Department of Mathematics, National University of Singapore, Singapore 119076, Singapore
- MR Author ID: 1075489
- Email: mathlqwang@163.com; wangliuquan@u.nus.edu
- Received by editor(s): October 29, 2016
- Received by editor(s) in revised form: June 19, 2017
- Published electronically: December 4, 2017
- Communicated by: Ken Ono
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1515-1528
- MSC (2010): Primary 05A17; Secondary 11F03, 11F33, 11P83
- DOI: https://doi.org/10.1090/proc/13858
- MathSciNet review: 3754338
Dedicated: Dedicated to Professor Heng Huat Chan on the occasion of his 50th birthday