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Research Article | Open Access

Some new identities for colored partitions with parts in multiples of 4

Roberta R. Zhou1( ), Fuquan Ren2
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Hebei 066004, China
School of Science, Yanshan University, Hebei 066004, China
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Abstract

To start, we provided the deformations of certain specific modular equations derived from Ramanujan's notebook, Part Ⅲ, by using the complete square formula. Subsequently, we established fifteen identities for partitions with distinct colors that arose from these deformed modular equations in the theory of modular equations. Throughout our investigation, we found that the fifteen identities have parts that were in multiples of 4.

Keywords

colored partitionsmodular equationstheta function identities
CLC number: Primary 11P84; Secondary 05A15, 05A17

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 26721-26740
DOI: 10.3934/math.20241300

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Cite this article:
Zhou RR, Ren F. Some new identities for colored partitions with parts in multiples of 4. AIMS Mathematics, 2024, 9(10): 26721-26740. https://doi.org/10.3934/math.20241300

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Received: 11 July 2024
Revised: 03 September 2024
Accepted: 05 September 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)