On the Coefficients of Cyclotomic Polynomials
Seiten
1993
American Mathematical Society (Verlag)
978-0-8218-2572-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2572-3 (ISBN)
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Studies the coefficients of cyclotomic polynomials. This book presents the principal result is an asymptotic formula for $/textnormal{log}a(m)$ that improves an estimate of Montgomery and Vaughan.
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.
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.
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.
| Erscheint lt. Verlag | 30.12.1993 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 198 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 0-8218-2572-0 / 0821825720 |
| ISBN-13 | 978-0-8218-2572-3 / 9780821825723 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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