New congruence properties for Ramanujan’s $\phi$ function
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- by Ernest X. W. Xia
- Proc. Amer. Math. Soc. 149 (2021), 4985-4999
- DOI: https://doi.org/10.1090/proc/15221
- Published electronically: September 27, 2021
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Abstract:
In 2012, Chan proved a number of congruences for the coefficients of Ramanujan’s $\phi$ function. In this paper, we prove some new congruences modulo powers of 2 and 3 for Ramanujan’s $\phi$ function by employing Newman’s identities and theta function identities.References
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Bibliographic Information
- Ernest X. W. Xia
- Affiliation: School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, Jiangsu Province 215009, People’s Republic of China
- Email: ernestxwxia@163.com
- Received by editor(s): March 8, 2020
- Received by editor(s) in revised form: May 13, 2020
- Published electronically: September 27, 2021
- Additional Notes: The author was supported by the National Science Foundation of China (no. 11971203) and the Natural Science Foundation of Jiangsu Province of China (no. BK20180044)
- Communicated by: Mourad Ismail
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 4985-4999
- MSC (2020): Primary 11P83; Secondary 05A17
- DOI: https://doi.org/10.1090/proc/15221
- MathSciNet review: 4327409