On Index Divisibility in the Orbit of Zero Generated by Polynomial Iteration

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dc.contributorBergmann, Bettina
dc.contributorDavidoff, Giuliana
dc.contributor.advisorRobinson, Margaret
dc.contributor.authorSchenck, Angelina
dc.date.accessioned2019-05-20T13:31:30Z
dc.date.available2019-05-20T13:31:30Z
dc.date.gradyear2019en_US
dc.date.issued2019-05-20
dc.description.abstractWe say that a sequence is a divisibility sequence if the n-th term divides the m-th term whenever n divides m. In 2007, Rice changed the course of papers related to divisibility sequences with his result in his undergraduate thesis at Harvey Mudd College that the orbit of zero of all polynomials without a linear term generates a rigid divisibility sequence. In 2017, Chen, Gassert, and Stange consider the index divisibility set of the orbit of zero of polynomials of monic polynomials. In a preprint, as a continuation of the previous paper, Gassert and Urbanski investigate the index divisibility set of the orbit of zero for monic polynomials with an additional term. In this thesis, we generalize many of the previous results to nonmonic polynomials. We provide full proofs of some of the previous known results where original authors supplied sketches and take into account the value of the leading coefficient. We also turn our attention toward divisibility sequences that are not rigid and conjecture how to adjust the results for rigid divisibility sequences to hold for nonrigid divisibility sequences.en_US
dc.description.sponsorshipMathematics & Statisticsen_US
dc.identifier.urihttp://hdl.handle.net/10166/5685
dc.language.isoen_USen_US
dc.rights.restrictedrestricteden_US
dc.subjectMathematicsen_US
dc.subjectNumber Theoryen_US
dc.subjectArithmetic Dynamicsen_US
dc.titleOn Index Divisibility in the Orbit of Zero Generated by Polynomial Iterationen_US
dc.typeThesis
mhc.degreeUndergraduateen_US
mhc.institutionMount Holyoke College

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