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dc.contributor.authorBeck, Michael Christopher
dc.date.accessioned2014-03-03T21:08:48Z
dc.date.available2014-03-03T21:08:48Z
dc.date.issued2004-05
dc.identifier.otherbeck_michael_c_200405_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/beck_michael_c_200405_phd
dc.identifier.urihttp://hdl.handle.net/10724/21426
dc.description.abstractWe begin by motivating and explaining the notion of square dependence. Then, given a sequence S = {s1, . . . , sj} composed of integers chosen independently and with uniform distribution from {1, . . . , n}, we want to know how likely S is to be square dependent. We then ask how many subsets I {1, . . . , j} we should expect for which Qi2I si is a square. To answer this, we find bounds on the function a(n, k), which counts the number of such subsets I of size k. We do this for a few small specific choices of k, and then in a more general setting prove both an upper bound and, for a smaller range of k, a lower bound. We then apply this work to get the asymptotic for the original expected value. Finally, we describe an algorithm for finding integer solutions to x3 + y3 + z3 = k for specific values of k, and present our computational results.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjectAnalytic Number Theory
dc.subjectFactoring Algorithm
dc.subjectSquare Dependence
dc.subjectQuadratic Sieve
dc.titleSquare dependence in random integers
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorAndrew Granville
dc.description.committeeAndrew Granville
dc.description.committeeEd Azoff
dc.description.committeeRodney Canfield
dc.description.committeeDino Lorenzini
dc.description.committeeRobert Rumely


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