Flat Cyclotomic Polynomials

Abstract

In the thesis, cyclotomic polynomials with only 0,1,-1 as coefficients are studied. Such a cyclotomic polynomial is called flat. It turns out that whether the n'th cyclotomic polynomial has this depends only on what primes divide n. The number of primes dividing n is defined to be the order of the n'th cyclotomic polynomial. We explain results from other papers, which state that every cyclotomic polynomial of order 2 is flat and we give infinite families of flat cyclotomic polynomials of order three and four.