Abstract:In this paper, we study sign changes and vanishing for the number of representations of an integer as a sum of triangular numbers plus three-colored sums of generalized pentagonal numbers with an even number of parts minus those with an odd number of parts. We study this by investigating coefficients appearing in the $q$-series expansion of $F(z) = \frac{\eta(z)}{{\eta(2z)}^2 {\eta(3z)}^3}$, where $\eta$ is the Dedekind-eta function. We use the Hardy-Ramanujan-Rademacher circle method to give an asymptotic formula for the coefficients.
From: Ben Kane [view email]
[v1]
Mon, 15 Jun 2026 04:43:05 UTC (105 KB)
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