Truncated Jacobi triple product series

Chun Wang; Ae Ja Yee

doi:10.1016/j.jcta.2019.03.003

Truncated Jacobi triple product series

Chun Wang, Ae Ja Yee

Mathematics

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

In their study of truncated theta series, Andrews-Merca and Guo-Zeng made a conjecture on Jacobi's triple product identity, which is settled by Mao and Yee independently. In this paper, we reprove this ex-conjecture by providing an explicit series form with nonnegative coefficients, which is reminiscent of the results of Andrews-Merca and Guo-Zeng. We also provide a companion theorem to this ex-conjecture.

Original language	English (US)
Pages (from-to)	382-392
Number of pages	11
Journal	Journal of Combinatorial Theory. Series A
Volume	166
DOIs	https://doi.org/10.1016/j.jcta.2019.03.003
State	Published - Aug 2019

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2019.03.003

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title = "Truncated Jacobi triple product series",

abstract = "In their study of truncated theta series, Andrews-Merca and Guo-Zeng made a conjecture on Jacobi's triple product identity, which is settled by Mao and Yee independently. In this paper, we reprove this ex-conjecture by providing an explicit series form with nonnegative coefficients, which is reminiscent of the results of Andrews-Merca and Guo-Zeng. We also provide a companion theorem to this ex-conjecture.",

author = "Chun Wang and Yee, {Ae Ja}",

note = "Funding Information: The authors are very grateful to the anonymous referee for his/her valuable comments and suggestions. The first author was partially supported by the outstanding doctoral dissertation cultivation plan of action (No. YB2016028 ). The second author was partially supported by a grant (# 280903 ) from the Simons Foundation . Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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AU - Yee, Ae Ja

N1 - Funding Information: The authors are very grateful to the anonymous referee for his/her valuable comments and suggestions. The first author was partially supported by the outstanding doctoral dissertation cultivation plan of action (No. YB2016028 ). The second author was partially supported by a grant (# 280903 ) from the Simons Foundation . Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/8

Y1 - 2019/8

N2 - In their study of truncated theta series, Andrews-Merca and Guo-Zeng made a conjecture on Jacobi's triple product identity, which is settled by Mao and Yee independently. In this paper, we reprove this ex-conjecture by providing an explicit series form with nonnegative coefficients, which is reminiscent of the results of Andrews-Merca and Guo-Zeng. We also provide a companion theorem to this ex-conjecture.

AB - In their study of truncated theta series, Andrews-Merca and Guo-Zeng made a conjecture on Jacobi's triple product identity, which is settled by Mao and Yee independently. In this paper, we reprove this ex-conjecture by providing an explicit series form with nonnegative coefficients, which is reminiscent of the results of Andrews-Merca and Guo-Zeng. We also provide a companion theorem to this ex-conjecture.

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JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

ER -

Truncated Jacobi triple product series

Abstract

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