On the Coefficients of Cyclotomic Polynomials

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On the Coefficients of Cyclotomic...

On the Coefficients of Cyclotomic Polynomials

Gennady Bachman

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

الفئات:

Mathematics

عام:

1993

الناشر:

Amer Mathematical Society

اللغة:

english

الصفحات:

ISBN 10:

0821825720

ISBN 13: