Special cubic zeros and the dual variety
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929468269920256 |
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| author | Wang, Victor Y. |
| author_facet | Wang, Victor Y. |
| contents | Let $F$ be a diagonal cubic form over $\mathbb{Z}$ in $6$ variables. From the dual variety in the delta method of Duke--Friedlander--Iwaniec and Heath-Brown, we unconditionally extract a weighted count of certain special integral zeros of $F$ in regions of diameter $X \to \infty$. Heath-Brown did the same in $4$ variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_03396 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Special cubic zeros and the dual variety Wang, Victor Y. Number Theory Algebraic Geometry Let $F$ be a diagonal cubic form over $\mathbb{Z}$ in $6$ variables. From the dual variety in the delta method of Duke--Friedlander--Iwaniec and Heath-Brown, we unconditionally extract a weighted count of certain special integral zeros of $F$ in regions of diameter $X \to \infty$. Heath-Brown did the same in $4$ variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general $F$. |
| title | Special cubic zeros and the dual variety |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2108.03396 |