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

Nava Kayla Balsam

Title:
The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields
Author(s):
Balsam, Nava Kayla
Thesis Advisor(s):
Goldfeld, Dorian
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
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.
Subject(s):
Mathematics
Item views
379
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Suggested Citation:
Nava Kayla Balsam, , The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields, Columbia University Academic Commons, .

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