Some Properties of the Coefficients of Cyclotomic Polynomials

Author: Lu, Kau-un

Year: 1968

Degree: Dissertation (Ph.D.)

Advisor: Apostol, Tom M.

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/py5s-v205

Abstract

An explicit formula is obtained for the coefficients of the cyclotomic polynomial Fn(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 Fn(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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