Rational Points of Bounded Height on Some Genus Zero Modular Curves
Issue Date
2023Keywords
arithmetic geometryDrinfeld modules
elliptic curves
heights
number theory
weighted projective stacks
Advisor
Cais, Bryden R.Metadata
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The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
We prove several results related to counting points of bounded height on weighted projectivestacks. We then apply these results to study the arithmetic statistics of elliptic curves and Drinfeld modules. For example, we give asymptotics for the number of elliptic curves (or Drinfeld modules) which satisfy a set of local conditions or a which admit a prescribed level structure. Using our results for counting elliptic curves satisfying local conditions we are able to give a conditional upper bound for the average rank of elliptic curves over arbitrary number fields.Type
Electronic Dissertationtext
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMathematical Sciences