Computational Excursions in Analysis and Number Theory

1. Auflage. Softcover version of original hardcover Auflage 2002
ISBN: 978-1-4419-3000-2
Verlag: Humana

Buch, Englisch, 220 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 359 g

Reihe: CMS Books in Mathematics

This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.

Zielgruppe

Research

Autoren/Hrsg.

Borwein, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

1 Introduction.- 2 LLL and PSLQ.- 3 Pisot and Salem Numbers.- 4 Rudin-Shapiro Polynomials.- 5 Fekete Polynomials.- 6 Products of Cyclotomic Polynomials.- 7 Location of Zeros.- 8 Maximal Vanishing.- 9 Diophantine Approximation of Zeros.- 10 The Integer Chebyshev Problem.- 11 The Prouhet-Tarry-Escott Problem.- 12 The Easier Waring Problem.- 13 The Erd?s-Szekeres Problem.- 14 Barker Polynomials and Golay Pairs.- 15 The Littlewood Problem.- 16 Spectra.- A A Compendium of Inequalities.- B Lattice Basis Reduction and Integer Relations.- C Explicit Merit Factor Formulae.- D Research Problems.