The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields
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.
Academic Commons
Balsam, Nava Kayla
Author
Goldfeld, Dorian
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2015
eng
2017-06-12T17:37:29Z
2017-11-10T08:17:10Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D87P8XF4