A Survey on Coefficients of Cyclotomic Polynomials

TL;DR

This survey reviews the extensive research on the properties of cyclotomic polynomial coefficients, highlighting recent developments and consolidating key results and references in this mathematically significant area.

Contribution

It compiles and summarizes the main results and references on cyclotomic polynomial coefficients, emphasizing recent research trends and findings.

Findings

Summary of key properties of cyclotomic polynomial coefficients

Compilation of recent research results

References to foundational and recent proofs

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).