Proof of a conjecture of Andrews and Bachraoui on a Hecke sum

Koustav Banerjee; Kathrin Bringmann

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arXiv · 2605.10300

Proof of a conjecture of Andrews and Bachraoui on a Hecke sum

Koustav Banerjee·Kathrin Bringmann

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Abstract

In this paper, we prove a conjecture of Andrews and Bachraoui relating a generating function arising from two-color partitions (with odd smallest part and restrictions on the even parts) to a Hecke-type double sum. Our proof is based on Zwegers' theory of indefinite theta functions together with modular transformation properties of mock theta functions.

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Koustav Banerjee, Kathrin Bringmann. 2026-05-11. Proof of a conjecture of Andrews and Bachraoui on a Hecke sum. https://arxiv.org/abs/2605.10300

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