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arXiv · 1812.06458

Several $q$-series related to Ramanujan's theta functions

Dazhao Tang·Ernest. X. W. Xia
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Abstract

Quite recently, the first author investigated vanishing coefficients of the arithmetic progressions in several $q$-series expansions. In this paper, we further study the signs of coefficients in two $q$-series expansions and establish some arithmetic relations for several $q$-series expansions by means of Ramanujan's theta functions. We obtain the 5-dissections of these two $q$-series and give combinatorial interpretations for these dissections. Moreover, we obtain four $q$-series identities involving the aforementioned $q$-series, two of which were proved by Kim and Toh via modular forms.

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Dazhao Tang, Ernest. X. W. Xia. 2018-12-16. Several $q$-series related to Ramanujan's theta functions. https://arxiv.org/abs/1812.06458

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