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arXiv · 2604.08013

Proofs for Andrews' Conjectures 5 and 6 on $v_1(q)$

Mohamed El Bachraoui
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Abstract

Folsom, Males, Rolen, and Storzer recently proved Andrews' Conjecture~4 for the coefficients of \[ v_1(q)=\sum_{n\ge 0}\frac{q^{n(n+1)/2}}{(-q^2;q^2)_n}=\sum_{n\ge 0}V_1(n)q^n. \] They also proved a refined density-one version of Andrews' Conjecture~3. In this paper we prove Andrews' Conjectures~5 and~6. Our proof relies on an investigation of the simple zeros of the trigonometric factor in the Folsom--Males--Rolen--Storzer asymptotic and showing that the relevant quadratic sequence stays a positive distance from the integers infinitely often. The argument is unconditional.

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Mohamed El Bachraoui. 2026-04-09. Proofs for Andrews' Conjectures 5 and 6 on $v_1(q)$. https://arxiv.org/abs/2604.08013

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