Proofs for Andrews' Conjectures 5 and 6 on $v_1(q)$
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911578379517952 |
|---|---|
| author | Bachraoui, Mohamed El |
| author_facet | Bachraoui, Mohamed El |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08013 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proofs for Andrews' Conjectures 5 and 6 on $v_1(q)$ Bachraoui, Mohamed El Number Theory 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. |
| title | Proofs for Andrews' Conjectures 5 and 6 on $v_1(q)$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.08013 |