Number-theoretic properties of the binomial distribution with applications in arithmetic geometry
| dc.contributor.author | Schmidt, Eric, author | |
| dc.contributor.author | Achter, Jeffrey, advisor | |
| dc.contributor.author | Pries, Rachel, committee member | |
| dc.contributor.author | Cavalieri, Renzo, committee member | |
| dc.contributor.author | Bohm, Wim, committee member | |
| dc.date.accessioned | 2007-01-03T06:33:12Z | |
| dc.date.available | 2007-01-03T06:33:12Z | |
| dc.date.issued | 2014 | |
| dc.description.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. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Schmidt_colostate_0053A_12580.pdf | |
| dc.identifier.uri | http://hdl.handle.net/10217/83813 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| 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. | |
| dc.subject | binomial distribution | |
| dc.subject | squarefree | |
| dc.subject | complete intersection | |
| dc.title | Number-theoretic properties of the binomial distribution with applications in arithmetic geometry | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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