Extension of a proof of the Ramanujan congruences for multipartitions

2016/01/20 by Lazarev, Oleg, Mizuhara, Matthew S., Reid, Benjamin +1
#11P83 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1601.05287

Abstract

Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function p(n). Their proof uses only the classical theory of modular forms as well as a beautiful result of Choie, Kohnen, and Ono, without need for Hecke operators. In this paper we give a method for generalizing Lachterman, Schayer, and Younger's proof to include Ramanujan congruences for multipartition functions p_k(n), and Ramanujan congruences for p(n) modulo certain prime powers.

Related

• Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function
• Congruences of Multipartition Functions Modulo Powers of Primes
• Ramanujan congruences for overpartitions with restricted odd differences
• Arithmetic properties of generalized Frobenius partitions
• Ramanujan Congruences for Fractional Partition Functions