On The Coefficients Of Cyclotomic Polynomials Gennady Bachman

ISBN: 9780821825723

Published: January 1st 1993

Unknown Binding

80 pages


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On The Coefficients Of Cyclotomic Polynomials  by  Gennady Bachman

On The Coefficients Of Cyclotomic Polynomials by Gennady Bachman
January 1st 1993 | Unknown Binding | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 80 pages | ISBN: 9780821825723 | 5.26 Mb

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



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