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

Folsom, Males, Rolen, and Storzer recently proved Andrews’ Conjecture~4 for the coefficients of $$v_1(q)=\sum _{n\ge 0}\frac{q^{n(n+1)\mathrm{/}2}}{(-q^2;q^2{)}_n}=\sum _{n\ge 0}{V}_1(n)q^n\mathrm{.}$$ 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.