Number-theoretic properties of the binomial distribution with applications in arithmetic geometry
Date
2014
Authors
Schmidt, Eric, author
Achter, Jeffrey, advisor
Pries, Rachel, committee member
Cavalieri, Renzo, committee member
Bohm, Wim, committee member
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Abstract
Alina Bucur et al. showed that the distribution of the number of points on a smooth projective plane curve of degree d over a finite field of order q is approximated by a particular binomial distribution. We generalize their arguments to obtain a similar theorem concerning hypersurfaces in projective m-space. We briefly describe Bucur and Kedlaya's generalization to complete intersections. We then prove theorems concerning the probability that a binomial distribution yields an integer of various certain properties, such as being prime or being squarefree. Finally, we show how to apply such a theorem, concerning a property P, to yield results concerning the probability that the numbers of points on random complete intersections possess property P.
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Subject
binomial distribution
squarefree
complete intersection