On the Coefficients of Cyclotomic Polynomials (Memoirs of the American Mathematical Society)

On the Coefficients of Cyclotomic Polynomials (Memoirs of the American Mathematical Society)

By: Gennady Bachman (author)Paperback

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Description

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.

Contents

Introduction Statement of results Proof of Theorem 0; upper bound Preliminaries Proof of Theorem 1; the minor arcs estimate Proof of Theorem 1; the major arcs estimate Proof of Theorem 2; preliminaries Proof of Theorem 2; completion Proof of Propositions 1 and 2 Proof of Theorem 3 Appendix References.

Product Details

  • ISBN13: 9780821825723
  • Format: Paperback
  • Number Of Pages: 80
  • ID: 9780821825723
  • ISBN10: 0821825720

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