Ramanujan Type Congruences for a Partition Function

Haijian Zhao, Zheyuan Zhong

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Source: Crossref

Published: Mar 11, 2011

DOI: 10.37236/545

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Source abstract

We investigate the arithmetic properties of a certain function $b(n)$ given by $\sum\limits_{n=0}^\infty b(n)q^n=(q;q)_\infty^{-2}(q^2;q^2)_\infty^{-2}$ . One of our main results is $b(9n+7)\equiv 0\ ({\rm mod\ }9)$ .

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Ramanujan Type Congruences for a Partition Function — Mathematical Frontier Network