Number Theory Seminar

Speaker: James Parks (University of Lethbridge)

Title: Averages of elliptic curves over finite fields

Abstract: Let E be an elliptic curve defined over Q. If p is a prime of good reduction then the points on the reduced elliptic curve modulo p forms a group. In this talk we consider two functions defined on the primes. In particular, we define a function that counts the number of primes such that the size of the group mod p is a fixed integer N and a function that counts pairs of distinct primes (p, q) that we call amicable pairs. We present results on the averages of these functions over a family of elliptic curves.