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dc.contributor.authorAl-Shaghay, Abdullah
dc.date.accessioned2019-12-16T17:11:14Z
dc.date.available2019-12-16T17:11:14Z
dc.identifier.urihttp://hdl.handle.net/10222/76815
dc.description.abstractFor a positive integer n the nth cyclotomic polynomial can be written as Φn(x)=∏︂(x−e^{2pi k/n} ). k∈(Z/nZ)^{×} When n = p is an odd prime, the nth cyclotomic polynomial has the special form Φp(x)=∑︂x^{k} =x^{p−1} +x^{p−2} +...+x+1. These two representations of the cyclotomic polynomials highlight the roots of Φn(x) and the coefficients of Φn(x), respectively. Continuing with the work of Kwon, J. Lee, and K. Lee and Harrington we investigate the generalization of the cyclotomic polynomials in two distinct ways; one affecting the roots of Φn(x) and the other affecting the coefficients of Φn(x). In the final chapter of the thesis we discuss congruences for particular binomial sums and use those congruences to prove results concerning two special cases of Jacobi polynomials, the Chebyshev polynomials and the Legendre polynomials.en_US
dc.language.isoenen_US
dc.subjectMathematicsen_US
dc.titleSOME CLASSES OF GENERALIZED CYCLOTOMIC POLYNOMIALSen_US
dc.date.defence2019-12-10
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.degreeDoctor of Philosophyen_US
dc.contributor.external-examinerDr. Michael Filasetaen_US
dc.contributor.graduate-coordinatorDr. David Ironen_US
dc.contributor.thesis-readerDr. Keith Johnsonen_US
dc.contributor.thesis-readerDr. Rob Nobleen_US
dc.contributor.thesis-supervisorDr. Karl Dilcheren_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.manuscriptsNot Applicableen_US
dc.contributor.copyright-releaseNot Applicableen_US
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