Rank differences for overpartitions modulo $6$
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- by Bin Wei and Helen W. J. Zhang
- Proc. Amer. Math. Soc. 148 (2020), 4333-4349
- DOI: https://doi.org/10.1090/proc/15075
- Published electronically: June 1, 2020
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Abstract:
In this article, we study the $3$-dissection properties of ranks for overpartitions modulo $6$. In this case, $-1$ appears as a unit root, so that double poles occur in the generating function. We prove two identities of generalized Lambert series by taking limits in Chan’s identities, which are useful in generating various formulas with similar poles. We also relate these ranks to the third order mock theta functions $\omega (q)$ and $\rho (q)$.References
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Bibliographic Information
- Bin Wei
- Affiliation: Center for Applied Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
- MR Author ID: 1011181
- Email: bwei@tju.edu.cn
- Helen W. J. Zhang
- Affiliation: School of Mathematics, Hunan University, Changsha 410082, People’s Republic of China
- MR Author ID: 1241719
- Email: helenzhang@hnu.edu.cn
- Received by editor(s): October 5, 2019
- Received by editor(s) in revised form: February 14, 2020
- Published electronically: June 1, 2020
- Additional Notes: The authors were supported by NSFC (Grant No. 11701412). The second author was supported by the Fundamental Research Funds for the Central Universities (Grant No. 531118010411).
The second author is the corresponding author. - Communicated by: Mourad Ismail
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4333-4349
- MSC (2010): Primary 33D15, 05A17, 11P81, 11F37
- DOI: https://doi.org/10.1090/proc/15075
- MathSciNet review: 4135301