Pinned distance sets, Wolff's exponent in finite fields and improved sum-product estimates
| dc.creator | Hart, Derrick | |
| dc.creator | Iosevich, Alex | |
| dc.date | 2007-11-28 | |
| dc.date.accessioned | 2026-07-07T08:45:57Z | |
| dc.date.available | 2026-07-07T08:45:57Z | |
| dc.description | An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold $α>0$ such that $|Δ(E)| \gtrsim q$ whenever $|E| \gtrsim q^α$, where $E \subset {\Bbb F}_q^d$, the $d$-dimensional vector space over a finite field with $q$ elements (not necessarily prime). Here $Δ(E)=\{{(x_1-y_1)}^2+...+{(x_d-y_d)}^2: x,y \in E\}$. The second listed author and Misha Rudnev established the threshold $\frac{d+1}{2}$, and the authors of this paper, Doowon Koh and Misha Rudnev proved that this exponent is sharp in even dimensions. In this paper we improve the threshold to $\frac{d^2}{2d-1}$ under the additional assumption that $E$ has product structure. In particular, we obtain the exponent 4/3, consistent with the corresponding exponent in Euclidean space obtained by Wolff. | |
| dc.identifier | https://arxiv.org/abs/0711.4597 | |
| dc.identifier | http://arxiv.org/abs/0711.4597 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143126 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.title | Pinned distance sets, Wolff's exponent in finite fields and improved sum-product estimates | |
| dc.type | text |