Theses Doctoral

The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields

Balsam, Nava Kayla

The parity of the analytic rank of an elliptic curve is given by the root number in the functional equation L(E,s). Fixing an elliptic curve over any number eld and considering the family of its quadratic twists, it is natural to ask what the average analytic rank in this family is. A lower bound on this number is given by the average root number.

In this paper, we investigate the root number in such families and derive an asymptotic formula for the proportion of curves in the family that have even rank. Our results are then used to support a conjecture about the average analytic rank in this family of elliptic curves.


  • thumnail for Balsam_columbia_0054D_12564.pdf Balsam_columbia_0054D_12564.pdf application/pdf 819 KB Download File

More About This Work

Academic Units
Thesis Advisors
Goldfeld, Dorian
Ph.D., Columbia University
Published Here
May 7, 2015