The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields
By: Nava Kayla Balsam
Publisher: [publisher not identified]
Published: 2015
Place of publication: [New York, N.Y.?]
Language: eng
Description: 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.
Notes: Department: Mathematics.

Thesis advisor: Dorian Goldfeld.

Thesis (Ph.D.)--Columbia University, 2015.