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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Maße
Höhe: 255 mm
Breite: 180 mm
Gewicht
ISBN-13
978-0-8218-2572-3 (9780821825723)
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Schweitzer Klassifikation
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.
