Title: Frobenius fields for elliptic curves
Speaker: Alina Cojocaru
Speaker Info: UIC
Brief Description:
Special Note:
Abstract:
Let E be an elliptic curve defined over Q. For a prime p of good reduction for E, let pi_p be the p-Weil root of E and Q(pi_p) the associated imaginary quadratic field generated by pi_p. In 1976, Serge Lang and Hale Trotter formulated a conjectural asymptotic formula for the number of primes p < x for which Q(pi_p) is isomorphic to a fixed imaginary quadratic field. I will discuss progress on this conjecture, in particular an average result confirming the predicted asymptotic formula. The latter is joint work with Henryk Iwaniec and Nathan Jones.Date: Monday, April 29, 2013