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A partition of n is l-regular if none of its parts is divisible by l. Let b l (n) denote the number of l-regular partitions of n. In this paper, using theta function identities due to Ramanujan, we establish some new infinite families of congruences for b l (n) modulo l, where l = 17, 23, and for b 65 (n) modulo 13.
A partition of n is l-regular if none of its parts is divisible by l. Let b l (n) denote the number of l-regular partitions of n. In this paper, using the theory of Hecke eigenforms explored by J.-P. Serre, we establish exact criteria for the 3-divisibility of b 9 (n) and b 27 (n).2010 Mathematics Subject Classification. 11P83.
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