Schmidt, Eric, authorAchter, Jeffrey, advisorPries, Rachel, committee memberCavalieri, Renzo, committee memberBohm, Wim, committee member2007-01-032007-01-032014http://hdl.handle.net/10217/83813Alina 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.born digitaldoctoral dissertationsengCopyright 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.binomial distributionsquarefreecomplete intersectionText