Congruences for Andrews' spt-function modulo powers of 5, 7 and 13

2010/11/09 by Frank Garvan, Garvan, F. G. · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1011.1955

Abstract

Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan's partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type congruences for spt(n) modulo p for all primes p>3 which were conjectured earlier by the author. We extend Ono's method to handle the powers of 5, 7 and 13 congruences. We need the theory of weak Maass forms as well as certain classical modular equations for the Dedekind eta-function.

Citations

• On Modular Forms of Half Integral Weight

Cited by

• Recurrence and congruences for the smallest parts function

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