On the Coefficients of Cyclotomic Polynomials

ISBN-13: 9780821825723 / Angielski / Miękka / 1993 / 80 str.

Opis

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 $a(m)={ m max _n vert a(m, n)vert$. The principal result is an asymptotic formula for ${ m log a(m)$ that improves a recent estimate of Montgomery and Vaughan. Bachman also gives similar formulae for the logarithms of the one-sided extrema $a (m)={ m max _na(m, n)$ and $a_*(m)={ m min _na(m, n)$. In the course of the proof, estimates are obtained for certain exponential sums which are of independent inter