On the coefficients of cyclotomic polynomials / Gennady Bachman.

Format:

Book

Author/Creator:

Bachman, Gennady, 1959- author.

Series:

Memoirs of the American Mathematical Society ; Volume 106, Number 510.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 106, Number 510

Language:

English

Subjects (All):

Exponential sums.

Cyclotomy.

Polynomials.

Physical Description:

1 online resource (93 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1993.

Language Note:

English

Summary:

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 ${\rm log a(m)$ 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 interest.

Contents:

""Contents""; ""0. Introduction""; ""1. Statement of results""; ""2. Proof of Theorem 0; the upper bound""; ""3. Preliminaries""; ""4. Proof of Theorem 1; the minor arcs estimate""; ""5. Proof of Theorem 1; the major arcs estimate""; ""6. Proof of Theorem 2; preliminaries""; ""7. Proof of Theorem 2; completion""; ""8. Proof of Propositions 1 and 2""; ""9. Proof of Theorem 3""; ""Appendix""; ""References""

Notes:

"November 1993, Volume 106, Number 510 (fifth of 6 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0087-1