Asymptotic formulas for general colored partition functions

2016/10/19 by Yong-Gao Chen, Chen, Yong-Gao, Ya-Li Li +1
Mathematics · #05A17 #11N37 #11P82 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1610.05938

openalex publication_date 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1917, Hardy and Ramanujan obtained the asymptotic formula for the classical partition function p(n). The classical partition function p(n) has been extensively studied. Recently, Luca and Ralaivaosaona obtained the asymptotic formula for the square-root function. Many mathematicians have paid much attention to congruences on some special colored partition functions. In this paper, we investigate the general colored partition functions. Given positive integers 1=s₁

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