Work

Limit theorems for Andrews’ restricted overpartitions

Year: 2026

Type: article

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.

Source: The Ramanujan Journal

DOI: 10.1007/s11139-025-01313-1

Authors: Tapas Bhowmik, Alex Cao, Jack Frew, John Lehman, Wei-Lun Tsai

Institutions: University of South Carolina, University of California, Santa Barbara, The Ohio State University, Durham University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

OpenAlex ID: W7129567450