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Title: A Bound on The Average Rank of j-Invariant Zero Elliptic Curves
Authors: Ruth, Samuel
Advisors: Bhargava, Manjul
Contributors: Mathematics Department
Keywords: Arithmetic Statistics
Circle Method
Elliptic Curves
Number theory
Subjects: Mathematics
Issue Date: 2013
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, we prove that the average rank of j-invariant 0 elliptic curves, when ordered by discriminant, is bounded above by 3. This work follows from work of Bhargava and Shankar relating elements of the 2-Selmer groups of elliptic curves with equivalence classes of certain binary quartic forms. We also count the number of equivalence classes of these binary quartic forms. This step involves counting the number of points on a quadric in a homogenously expanding non-compact region. To count the number of points on this quadric, we use a modified version of the circle method. This work also has an application to the statistics of the class group of certain pure cubic fields.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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