Asymptotics of Certain q-Series

2018/12/08 by Ruiming Zhang, Zhang, Ruiming
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1901.01109

openalex publication_date 2018/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we study complete asymptotic expansions for the q-series ∑_n=1^∞\frac1n^bq^n^a and ∑_n=1^∞\fracσ_α(n)n^bq^n^a in the scale function (log q)ⁿ as q→1^-, where a>0, q∈(0,1), b,α∈ℂ and σ_α(n) is the divisor function σ_α(n)=∑_{d\vert n}d^α.

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