AN EXPLICIT INCIDENCE THEOREM IN Fp

Let P = A x A subset of F-p x F-p, p a prime. Assume that P = A x A has n elements, n < p. See P as a set of points in the plane over F-p. We show that the pairs of points in P determine >= cn(1+1/267) 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 < p) is bounded by Cn(3/2-1/10678), where C is an absolute constant.