Congruences of coefficients in expansions of non-Habiro ring elements

Authors

Ankush Goswami, The University of Texas Rio Grande Valley
Jeffery Opoku, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

12-29-2026

Abstract

In 2016, Andrews and Sellers studied the coefficients in the (1−q)-expansion of F(q), known as the Fishburn numbers, and established several congruences modulo primes. Motivated by their work, there has been considerable interest in extending these congruences to similar expansions of q-hypergeometric series within the Habiro ring that satisfy so-called “strange” identities. In this work, we establish a general result on prime-power congruences for coefficients arising from certain expansions of non-Habiro ring elements that also satisfy strange identities. As applications, we consider two such non-Habiro elements previously studied by Andrews et al. (Duke Math J 108(3):395–419, 2001), and show that the appropriately normalized coefficients in their expansions obey prime-power congruences.

Comments

https://rdcu.be/e4rih

Recommended Citation

Goswami, Ankush, and Jeffery Opoku. "Congruences of coefficients in expansions of non-Habiro ring elements: A. Goswami, J. Opoku." The Ramanujan Journal 69, no. 1 (2026): 24. https://doi.org/10.1007/s11139-025-01287-0

Publication Title

The Ramanujan Journal

DOI

10.1007/s11139-025-01287-0