Proof of a conjecture of Banerjee,Bringmann and Bachraoui on infinite families of congruences

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Détails bibliographiques
Auteurs principaux:	Sun, Junjie, Yao, Olivia X. M.
Format:	Preprint
Publié:	2026
Sujets:	Number Theory
Accès en ligne:	Acceder al recurso
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_version_	1866913009492819968
author	Sun, Junjie Yao, Olivia X. M.
author_facet	Sun, Junjie Yao, Olivia X. M.
contents	Recently, Andrews and Bachraoui investigated congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan type congruences and a vanishing identity for the limiting sequence. Very recently, Banerjee, Bringmann and Bachraoui confirmed these three conjectures by relating the corresponding generating function to modular forms and mock theta functions. At the end of their paper, they posed a conjecture on infinite families of congruences modulo 4 and 8 for the limiting sequence. The Banerjee-Bringmann-Bachraoui's conjecture implies the two conjectures given by Andrews and Bachraoui. In this note, we settle Banerjee-Bringmann-Bachraoui's conjecture on infinite famlies of congruences based on Banerjee-Bringmann-Bachraoui's results and an identity due to Waston.
format	Preprint
id	arxiv_https___arxiv_org_abs_2604_05403
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Proof of a conjecture of Banerjee,Bringmann and Bachraoui on infinite families of congruences Sun, Junjie Yao, Olivia X. M. Number Theory Recently, Andrews and Bachraoui investigated congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan type congruences and a vanishing identity for the limiting sequence. Very recently, Banerjee, Bringmann and Bachraoui confirmed these three conjectures by relating the corresponding generating function to modular forms and mock theta functions. At the end of their paper, they posed a conjecture on infinite families of congruences modulo 4 and 8 for the limiting sequence. The Banerjee-Bringmann-Bachraoui's conjecture implies the two conjectures given by Andrews and Bachraoui. In this note, we settle Banerjee-Bringmann-Bachraoui's conjecture on infinite famlies of congruences based on Banerjee-Bringmann-Bachraoui's results and an identity due to Waston.
title	Proof of a conjecture of Banerjee,Bringmann and Bachraoui on infinite families of congruences
topic	Number Theory
url	https://arxiv.org/abs/2604.05403

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