Computational Excursions in Analysis and Number Theory

Peter B. Borwein

220 pages, parution le 04/09/2002

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Résumé

This book is designed for a computationally intensive graduate course based around a collection of classical unsolved extremal problems for polynomials. These problems, all of which lend themselves to extensive computational exploration, live at the interface of analysis, combinatorics and number theory so the techniques involved are diverse. A main computational tool used is the LLL algorithm for finding small vectors in a lattice.
Many exercises and open research problems are included. Indeed one aim of the book is to tempt the able reader into the rich possibilities for research in this area.

Contents

Preface
Introduction
LLL and PSLQ
Pisot and Salem Numbers
Rudin-Shapiro Polynomials
Fekete Polynomials
Products of Cyclotomic Polynomials
Location of Zeros
Maximal Vanishing
Diophantine Approximation of Zeros
The Integer-Chebyshev Problem
The Prouhet-Tarry-Escott Problem
The Easier Waring Problem
The Erdös-Szekeres Problem
Barker Polynomials and Golay Pairs
The Littlewood Problem
Spectra
Appendix A: A Compendium of Inequalities
B: Lattice Basis Reduction and Integer Relations
C: Explicit Merit Factor Formulae
D: Research Problems
References
Index

L'auteur - Peter B. Borwein

Peter Borwein is Professor of Mathematics at Simon Fraser University and the Associate Director of the Centre for Experimental and Constructive Mathematics. He is also the recipient of the Mathematical Association of America Chauvenet Prize and the Merten M. Hasse Prize for expository writing in mathematics.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Peter B. Borwein
Parution	04/09/2002
Nb. de pages	220
Format	16 x 24
Couverture	Relié
Poids	450g
Intérieur	Noir et Blanc
EAN13	9780387954448
ISBN13	978-0-387-95444-8