@article{Zhou2024, 
author = {Roberta R. Zhou and Fuquan Ren},
title = {Some new identities for colored partitions with parts in multiples of  4},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {26721-26740},
keywords = {colored partitions, modular equations, theta function identities},
url = {https://www.sciopen.com/article/10.3934/math.20241300},
doi = {10.3934/math.20241300},
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.}
}