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An explicit incidence theorem in F_p | Harald Andres Helfgott
; Misha Rudnev
; | Date: |
12 Jan 2010 | Abstract: | Let $P = A imes A subset mathbb{F}_p imes mathbb{F}_p$, $p$ a prime.
Assume that $P= A imes A$ has $n$ elements, $n<p$. See $P$ as a set of points
in the plane over $mathbb{F}_p$. We show that the pairs of points in $P$
determine $geq c n^{1 + {1/232}}$ lines, where $c$ is an absolute constant.
We derive from this an incidence theorem: the number of incidences between a
set of $n$ points and a set of $n$ lines in the projective plane over $F_p$
($n<sqrt{p}$) is bounded by $C n^{{3/2}-{1/9278}}$, where $C$ is an absolute
constant. | Source: | arXiv, 1001.1980 | Services: | Forum | Review | PDF | Favorites |
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