Modular forms and $k$-colored generalized Frobenius partitions
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- by Heng Huat Chan, Liuquan Wang and Yifan Yang PDF
- Trans. Amer. Math. Soc. 371 (2019), 2159-2205 Request permission
Abstract:
Let $k$ and $n$ be positive integers. Let $c\phi _{k}(n)$ denote the number of $k$-colored generalized Frobenius partitions of $n$ and let $\mathrm {C}\Phi _k(q)$ be the generating function of $c\phi _{k}(n)$. In this article, we study $\mathrm {C}\Phi _k(q)$ using the theory of modular forms and discover new surprising properties of $\mathrm {C}\Phi _k(q)$.References
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Additional Information
- Heng Huat Chan
- Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
- Address at time of publication: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria
- MR Author ID: 365568
- Email: matchh@nus.edu.sg
- Liuquan Wang
- Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, People’s Republic of China
- MR Author ID: 1075489
- Email: mathlqwang@163.com; wangliuquan@u.nus.edu; wanglq@whu.edu.cn
- Yifan Yang
- Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan 10617
- MR Author ID: 633505
- Email: yangyifan@ntu.edu.tw
- Received by editor(s): June 9, 2017
- Received by editor(s) in revised form: October 12, 2017
- Published electronically: September 20, 2018
- Additional Notes: Liuquan Wang is the corresponding author
This work was completed during the first author’s stay at the Faculty of Mathematics, University of Vienna. The first author would like to thank his host, Professor C. Krattenthaler, for his hospitality and for providing an excellent research environment during his stay in Vienna.
The second author was supported by the National Natural Science Foundation of China (11801424), the Fundamental Research Funds for the Central Universities (Grant No. 1301–413000053) and a start-up research grant (No. 1301–413100048) of the Wuhan University.
The third author was partially supported by Grant 102-2115-M-009-001-MY4 of the Ministry of Science and Technology, Taiwan (R.O.C.) - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 2159-2205
- MSC (2010): Primary 05A17, 11F11; Secondary 11P83, 11F03, 11F33
- DOI: https://doi.org/10.1090/tran/7447
- MathSciNet review: 3894049
Dedicated: Dedicated to Professor George E. Andrews on the occasion of his 80th birthday