Andrews-Beck type congruences modulo powers of 5

The Ramanujan Journal - Trang 1-13 - 2024
Nankun Hong1, Renrong Mao2
1Center for Pure Mathematics, School of Mathematical Sciences, Anhui University, Hefei, People’s Republic of China
2Department of Mathematics, Soochow University, Suzhou, People’s Republic of China

Tóm tắt

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 obtained congruences for NT(m, k, n) modulo 11 and 13. More recently, the second author used 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.

Tài liệu tham khảo

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