Counting Square-full Solutions to $x+y=z$
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917196391776256 |
|---|---|
| author | Heath-Brown, D. R. |
| author_facet | Heath-Brown, D. R. |
| contents | We show that there are $O(B^{3/5-3/1555+\ep})$ triples $(x,y,z)$ of square-full integesr up to $B$ satisfying the equation $x+y=z$ for any fixed $\ep>0$. This is the first improvement over the `easy' exponent $3/5$, given by Browning and Van Valckenborgh. One new tool is a strong uniform bound for the counting function for equations $aX^3+bY^3=cZ^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07817 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting Square-full Solutions to $x+y=z$ Heath-Brown, D. R. Number Theory 11D45 We show that there are $O(B^{3/5-3/1555+\ep})$ triples $(x,y,z)$ of square-full integesr up to $B$ satisfying the equation $x+y=z$ for any fixed $\ep>0$. This is the first improvement over the `easy' exponent $3/5$, given by Browning and Van Valckenborgh. One new tool is a strong uniform bound for the counting function for equations $aX^3+bY^3=cZ^3$. |
| title | Counting Square-full Solutions to $x+y=z$ |
| topic | Number Theory 11D45 |
| url | https://arxiv.org/abs/2601.07817 |