{"id":{"repo_id":"colostate","oai_identifier":"oai:mountainscholar.org:10217/83813"},"canonical_url":"https://search.dev.ndltd.org/etd/colostate/oai:mountainscholar.org:10217/83813","repository":{"repo_id":"colostate","name":"Colorado State University","base_url":"https://api.mountainscholar.org/server/oai/request"},"display":{"title":"Number-theoretic properties of the binomial distribution with applications in arithmetic geometry","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. 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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.","abstract_has_math":false,"creators":["Schmidt, Eric, author","Achter, Jeffrey, advisor","Pries, Rachel, committee member","Cavalieri, Renzo, committee member","Bohm, Wim, committee member"],"institution":"Colorado State University. Libraries","degree_name":"Doctor of Philosophy (Ph.D.)","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-27T19:13:06Z","subjects":["binomial distribution","squarefree","complete intersection"],"languages":["eng","English"],"rights":["Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. 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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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["born digital","doctoral dissertations"]},{"key":"dc:title","label":"Title","values":["Number-theoretic properties of the binomial distribution with applications in arithmetic geometry"]}]}],"canonical_facts":{"dc:creator":["Schmidt, Eric, author","Achter, Jeffrey, advisor","Pries, Rachel, committee member","Cavalieri, Renzo, committee member","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. 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