Thursday, November 11
Milner 216, 1:00 PM
Title: On the distribution of distances between the points of affine curves over finite fields
Abstract: Let F_q be a finite field with q elements, Fbar an algebraic closure of F_q, and A^n(Fbar) an n-dimensional affine space over Fbar. Let C be an affine absolutely irreducible curve in A^n(Fbar). We interpret the points of C over F_q as points in the cube [-1,1]^(n-1). The main result of this paper is an asymptotic formula for the distribution of points of C in [-1,1]^(n-1) provided the characteristic p of F_q is large, while n, log_p(q) are fixed, and the degree of C is bounded. When p = q, this becomes a recent result of Cobeli and Zaharescu.