A Survey on Coefficients of Cyclotomic Polynomials

Abstract

Cyclotomic polynomials play an important role in several areas of mathematics and their study has a very long history, which goes back at least to Gauss (1801). In particular, the properties of their coefficients have been intensively studied by several authors, and in the last 10 years there has been a burst of activity in this field of research. This concise survey attempts to collect the main results regarding the coefficients of the cyclotomic polynomials and to provide all the relevant references to their proofs. Previous surveys on this topic were given by Lenstra (1979), Vaughan (1989), and Thangadurai (2000).