Year: 2025
Type: preprint
Abstract: We prove several congruences satisfied by the generalized cubic and generalized overcubic partition functions, recently introduced by Amdeberhan, Sellers, and Singh. We also prove infinite families of congruences modulo powers of $2$ and modulo $12$ satisfied by the generalized overcubic partitions, as well as some density results that they satisfy. We use both elementary $q$-series techniques as well as the theory of modular forms to prove our results.
Source: arXiv (Cornell University)
Institution: Ahmedabad University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979260638
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