Vanishing Coefficients of q^5n+r and q^7n+r in Certain Infinite q-series Expansions

2025/10/07 by M. P. Thejitha, Thejitha, M. P., S. N. Fathima +2
Mathematics · #Advanced Mathematical Identities #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Primary 33D15

paper · pdf · doi:10.48550/arxiv.2510.05929

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

Abstract

Motivated by the recent work of several authors on vanishing coefficients of the arithmetic progression in certain q-series expansion, we study some variants of these q-series and prove some comparable results. For instance, if ∑_n=0^∞c₁(n)qⁿ=(± q²,± q³; q⁵)_∞² ( q, q¹⁴; q¹⁵)_∞, then c₁(5n+3)=0.

Citations

• Vanishing coefficient results in four families of infinite q-products
• Asymptotics for the Taylor coefficients of certain infinite products

Related

• Vanishing coefficients in several q-series expansions related to the Rogers--Ramanujan continued fraction
• Vanishing coefficient results in four families of infinite q-products
• Asymptotics of Certain q-Series
• MacMahon's sums-of-divisors and allied q-series
• On the vanishing of coefficients of the powers of a theta function