Memoirs of the American Mathematical Society 1993; 80 pp; softcover Volume: 106 ISBN10: 0821825720 ISBN13: 9780821825723 List Price: US$32 Individual Members: US$19.20 Institutional Members: US$25.60 Order Code: MEMO/106/510
 This book studies the coefficients of cyclotomic polynomials. Let \(a(m,n)\) be the \(m\) th coefficient of the \(n\) th cyclotomic polynomial \(\Phi _n(z)\), and let \(a(m)=\mathrm{max}_n \vert a(m,n)\vert\). The principal result is an asymptotic formula for \(\mathrm{log}a(m)\) that improves a recent estimate of Montgomery and Vaughan. Bachman also gives similar formulae for the logarithms of the onesided extrema \(a^*(m)=\mathrm{max}_na(m,n)\) and \(a_*(m)=\mathrm{ min}_na(m,n)\). In the course of the proof, estimates are obtained for certain exponential sums which are of independent interest. Readership Research mathematicians. Table of Contents  Introduction
 Statement of results
 Proof of Theorem 0; upper bound
 Preliminaries
 Proof of Theorem 1; the minor arcs estimate
 Proof of Theorem 1; the major arcs estimate
 Proof of Theorem 2; preliminaries
 Proof of Theorem 2; completion
 Proof of Propositions 1 and 2
 Proof of Theorem 3
 Appendix
 References
