Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01db78tc06x
 Title: The average rank of elliptic curves over number fields Authors: Shankar, Arul Advisors: Bhargava, Manjul Contributors: Mathematics Department Subjects: MathematicsBaltic studies Issue Date: 2013 Publisher: Princeton, NJ : Princeton University Abstract: In joint work with Manjul Bhargava, we proved that the average rank of rational elliptic curves, when ordered by their heights, is bounded above by 1.5. This result was accomplished by using Bhargava's geometry-of-numbers methods to obtain asymptotics for the number of GL2 (Z)-orbits on integral binary quartic forms having bounded invariants. This thesis extends these methods and generalizes the counting results to the space of binary quartic forms over the ring of integers of any number field. As a consequence, we prove that the average rank of elliptic curves over any number field is at most 1.5. URI: http://arks.princeton.edu/ark:/88435/dsp01db78tc06x 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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