Some Properties of the Coefficients of Cyclotomic Polynomials

Citation

Lu, Kau-un (1968) Some Properties of the Coefficients of Cyclotomic Polynomials. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/py5s-v205. https://resolver.caltech.edu/CaltechTHESIS:12182015-163230212

Abstract

An explicit formula is obtained for the coefficients of the cyclotomic polynomial F_n(x), where n is the product of two distinct odd primes. A recursion formula and a lower bound and an improvement of Bang’s upper bound for the coefficients of F_n(x) are also obtained, where n is the product of three distinct primes. The cyclotomic coefficients are also studied when n is the product of four distinct odd primes. A recursion formula and upper bounds for its coefficients are obtained. The last chapter includes a different approach to the cyclotomic coefficients. A connection is obtained between a certain partition function and the cyclotomic coefficients when n is the product of an arbitrary number of distinct odd primes. Finally, an upper bound for the coefficients is derived when n is the product of an arbitrary number of distinct and odd primes.

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