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Several q-series related to Ramanujan’s theta functions

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 interlinked identities for several q -series expansions by mea...

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Bibliographic Details
Published in:The Ramanujan journal 2020-12, Vol.53 (3), p.705-724
Main Authors: Tang, Dazhao, Xia, Ernest. X. W.
Format: Article
Language:English
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Summary: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 interlinked identities 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.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-019-00187-4