Quasimodularity and Limiting Behavior for Variations of MacMahon Series

2025/05/12 by Nazaroglu, Caner, Pandey, Badri Vishal, Singh, Ajit · 3 citations
#05A17 #11F11 #11F37 #11P81 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.08035

Abstract

Motivated by the 1920's seminal work of Major MacMahon, Amdeberhan--Andrews--Tauraso recently introduced an infinite family of q-series \[ U_t(a;q):= ∑_1≤ n₁

Cited by

• A Generalization of MacMahon Series via Cyclotomic Polynomials
• Asymptotics of partition parts in arithmetic progressions
• Applications of Faà di Bruno's formula to partition traces

Related

• Limiting behaviour and modular completions of MacMahon-like q-series
• A Generalization of MacMahon Series via Cyclotomic Polynomials
• MacMahon's sums-of-divisors and allied q-series
• Remarks on MacMahon's q-series
• Recursive Formulas for MacMahon and Ramanujan q-series