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Title: The average rank of elliptic curves over number fields
Authors: Shankar, Arul
Advisors: Bhargava, Manjul
Contributors: Mathematics Department
Subjects: Mathematics
Baltic 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.
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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