Lethbridge Number Theory and Combinatorics Seminar: Amir Akbary

For a prime p, let n(p) be the number of solutions (x, y) of y^2 = x^3 + ax + b over the finite field F_p and let a(p) = p - n(p). In 1976, Serge Lang and Hale Trotter formulated a conjecture regarding the distribution of primes p for which a(p) = A for a fixed integer A. In this talk we give an exposition of this conjecture as it is given in the introduction of a paper of Katz (N.Katz, Lang-Trotter Revisited, Bulletin of the AMS, Vol. 46, No. 3, July 2009, pp. 413-457).