An infinite family of overpartition congruences mod powers of 2

2025/10/23 by Zhumagali Shomanov, Shomanov, Zhumagali, Frank Garvan +1
Mathematics · #11F03 #11P83 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2510.20175

openalex publication_date 2025/10/23 · openalex created_date 2025/10/25 · openalex updated_date 2026/07/28

Abstract

We prove an infinite family of Hecke-like congruences for the overpartition function modulo powers of 2. Starting from a recent identity of Garvan and Morrow and iterating Atkin's U₂ operator, we determine lower bounds on the 2-adic valuations of the coefficients that arise at each step. Our approach yields new modular equations relating the Hauptmoduln G₂ on Γ₀(2) and G₈ on Γ₀(8), together with explicit U₂-action formulas.

Citations

• Multiplicative congruences for Andrews's even parts below odd parts function and related infinite products

Related

• Arithmetic properties of overpartitions
• Some New Congruences Modulo Powers of 2 For (j,k)-Regular Overpartition
• Arithmetic properties modulo powers of 2 for overpartition k-tuples with odd parts
• Arithmetic Properties modulo powers of 2 and 3 for Overpartition k-Tuples with Odd Parts
• Congruence classes of 2-adic valuations of Stirling numbers of the second kind