Divisibility properties of weighted k-regular partitions
Abstract
Abstract We study a generalized class of weighted k -regular partitions defined by $$ \sum _{n=0}^{\infty } c_{k, r_1, r_2}(n) q^n = \prod _{n=1}^{\infty } \frac{(1 - q^{nk})^{r_1}}{(1 - q^n)^{r_2}}, $$ ∑ n = 0 ∞ c k , r 1 , r 2 ( n ) q n = ∏ n = 1 ∞ ( 1 - q nk ) r 1 ( 1 - q n ) r 2 , which extends the classical k -regular partition function $$b_k(n)$$ b k ( n ) . We establish new infinite families of Ramanujan-type congruences, divisibility results, and positive-density prime sets for which $$c_{k, r_1, r_2}(n)$$ c k , r 1 , r 2 ( n ) vanishes modulo a given prime.
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Functional Equations Stability Results
Publication details
- Journal / source
- The Ramanujan Journal
- Publisher
- Springer Science and Business Media LLC
- Volume
- 70
- Issue
- 4
- Publication date
- 1 August 2026
- Language
- EN