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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. http://resolver.caltech.edu/CaltechTHESIS:12182015-163230212

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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Apostol, Tom M.
Thesis Committee:
  • Unknown, Unknown
Defense Date:5 April 1968
Record Number:CaltechTHESIS:12182015-163230212
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:12182015-163230212
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9331
Collection:CaltechTHESIS
Deposited By: Leslie Granillo
Deposited On:21 Dec 2015 17:41
Last Modified:21 Dec 2015 17:41

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