Limit theorems for Andrews’ restricted overpartitions
Abstract
Abstract The study of overpartitions in recent years has been used to great effect in various fields, including hypergeometric series, q -series identities, and mathematical physics. We investigate the limiting distributions of the number of parts in a family of overpartitions of n , introduced by Andrews, where parts are counted with two different weights. Using Andrews’ identities and the saddle-point method, we establish two central limit theorems (CLTs) for the number of parts as $$n\rightarrow \infty ,$$ n → ∞ , corresponding to these weightings. We also derive explicit formulas for the mean and variance in each case.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- The Ramanujan Journal
- Volume
- 69
- Issue
- 3
- Publication date
- 17 February 2026
- Language
- EN