Bounds for the distribution of Frobenius traces associated to products of non-CM elliptic curves

Alina Carmen Cojocaru, University of Illinois at Chicago

Fields Number Theory Seminar
Date: Monday, February 8, 2021

Abstract: Let E1/\Q,…,Eg/\Q be elliptic curves over \Q, without complex multiplication and pairwise non-isogenous over \Q¯. For an integer t and a positive real number x, denote by πA(x,t) the number of primes p≤x, of good reduction for the abelian variety A:=E1×…×Eg, for which the Frobenius trace associated to the reduction of A modulo p equals t. We present unconditional and conditional upper bounds for πA(x,t). This is joint work with Tian Wang (University of Illinois at Chicago).