Ramanujan-style proof of $$p_{-3}(11n+7) \equiv 0\ (\mathrm{mod\ }11)$$ |
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Authors: | Bernard L S Lin |
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Institution: | 1.School of Sciences,Jimei University,Xiamen,China |
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Abstract: | In this note, we establish two identities of \((q;\,q)_\infty ^8\) by using Jacobi’s four-square theorem and two of Ramanujan’s identities. As an important consequence, we present one Ramanujan-style proof of the congruence \(p_{-3}(11n+7)\equiv 0\ (\mathrm{mod\ }11)\), where \(p_{-3}(n)\) denotes the number of 3-color partitions of n. |
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