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

2025/05/02 by Frank Garvan, Garvan, Frank, Morrow, Connor · 1 citation
Computer Science · Mathematics · #11F25 #11F37 #11P83 #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 11P82 #Secondary 05A30 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2505.01344

openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove multiplicative congruences mod 2¹² for George Andrews's partition function, EO(n), the number of partitions of n in which every even part is less than each odd part and only the largest even part occurs an odd number of times. We find analogous congruences for more general infinite products. These congruences are obtained using Fricke involutions and Newman's approach to half integer weight Hecke operators on eta quotients, and were inspired by Atkin's multiplicative congruences for the partition function.

Citations

• Congruences modulo powers of 5 and 7 for the crank and rank parity functions and related mock theta functions
• The Final Problem : An Account of the Mock Theta Functions

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• An infinite family of overpartition congruences mod powers of 2

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