The Distribution Of Coefficients Of Cyclotomic Polynomials And Some Identites

Cyclotomic polynomial is an important research object in number theory.Many scholars have obtained a lot of results on cyclotomic polynomials.In this thesis,based on these results,we obtain some properties about the distribution of coefficients of cyclotomic polynomials and some new identities.The main results are as follows:1.Provides the definition and related properties of cyclotomic polynomials and unitary cyclotomic polynomials;inverse cyclotomic polynomials and inverse unitary cyclotomic polynomials;Ramanujan sums and unitary Ramanujan sums.2.Under the certain condition of arithmetic series,it is proved that the coefficients of unitary cyclotomic polynomials,inverse cyclotomic polynomials and inverse unitary cyclotomic polynomials can cover the set of integers Z,respectively.3.Some new identities about unitary cyclotomic polynomials and unitary Ramanujan sums are obtained.