Timothy G. F. Jones
Published 2011-10-21, updated 2011-11-01Version 2
Let P be a set of points and $L$ a set of lines in (F_p)^2, with |P|,|L|\leq N and N<p. We show that P and L generate no more than C N^(3/2 - 1/806 + o(1)) incidences for some absolute constant C. This improves by an order of magnitude on the previously best-known bound of C N^(3/2 - 1/10678).
Comments: 10 pages, some typos corrected and a couple of points expanded on in v2
An improved sum-product inequality in fields of prime order
An explicit incidence theorem in F_p
On size Ramsey numbers for a pair of cycles
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