An application of random plane slicing to counting $\mathbb{F}_q$-points on hypersurfaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2017
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914817903689728 |
|---|---|
| author | Slavov, Kaloyan |
| author_facet | Slavov, Kaloyan |
| contents | Let $X$ be an absolutely irreducible hypersurface of degree $d$ in $\mathbb{A}^n$, defined over a finite field $\mathbb{F}_q$. The Lang-Weil bound gives an interval that contains $#X(\mathbb{F}_q)$. We exhibit explicit intervals, which do not contain $#X(\mathbb{F}_q)$, and which overlap with the Lang-Weil interval. In particular, we sharpen the best known lower and upper bounds for $#X(\mathbb{F}_q)$. The proof uses a combinatorial probabilistic technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_05062 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | An application of random plane slicing to counting $\mathbb{F}_q$-points on hypersurfaces Slavov, Kaloyan Algebraic Geometry 14G15 11G25 Let $X$ be an absolutely irreducible hypersurface of degree $d$ in $\mathbb{A}^n$, defined over a finite field $\mathbb{F}_q$. The Lang-Weil bound gives an interval that contains $#X(\mathbb{F}_q)$. We exhibit explicit intervals, which do not contain $#X(\mathbb{F}_q)$, and which overlap with the Lang-Weil interval. In particular, we sharpen the best known lower and upper bounds for $#X(\mathbb{F}_q)$. The proof uses a combinatorial probabilistic technique. |
| title | An application of random plane slicing to counting $\mathbb{F}_q$-points on hypersurfaces |
| topic | Algebraic Geometry 14G15 11G25 |
| url | https://arxiv.org/abs/1703.05062 |