Rational Points of Bounded Height on Some Genus Zero Modular Curves
weighted projective stacks
AdvisorCais, Bryden R.
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PublisherThe University of Arizona.
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AbstractWe 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.
Degree ProgramGraduate College