Number-theoretic properties of the binomial distribution with applications in arithmetic geometry

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.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Colorado State University. Libraries

Year dc:date.issued

2014

Authors dc:creator

• Schmidt, Eric, author
• Achter, Jeffrey, advisor
• Pries, Rachel, committee member
• Cavalieri, Renzo, committee member
• Bohm, Wim, committee member

• binomial distribution
• squarefree
• complete intersection

Statement dc:rights

• Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.25675/3.018572

OAI identifier oai:identifier

oai:mountainscholar.org:10217/83813