# On The Coefficients Of Cyclotomic Polynomials Gennady Bachman

#### 80 pages

Description 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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