Thursday, February 17
Milner 317, 1:00 PM
Title: The Lang-Trotter conjecture on average
Abstract: In this talk, I will review some basic facts about quadratic forms and elliptic curves. I will discuss the Lang-Trotter conjecture and a proof that the conjecture is true when one averages over certain families of curves. The Lang-Trotter conjecture can be stated as follows. Let E be an elliptic curve over the rationals. Let a_E(p) = p + 1 - #E(F_p). Then the Lang and Trotter conjectured that #{ p < x : a_E(p) = r } is asymptotic to C_{E,r}*sqrt(x)/log(x).