# On the Coefficients of Cyclotomic Polynomials

ISBN-10: 0821825720

ISBN-13: 9780821825723

Pub. Date: 12/01/1993

Publisher: American Mathematical Society

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

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## Overview

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 one-sided 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.

## Product Details

ISBN-13:
9780821825723
Publisher:
American Mathematical Society
Publication date:
12/01/1993
Series:
Memoirs of the American Mathematical Society Series, #51
Pages:
80
Product dimensions:
7.09(w) x 10.04(h) x (d)

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