Auxiliary Polynomials in Number Theory

Author: David Masser

Publisher: Cambridge University Press

ISBN: 1107061571

Category: Mathematics

Page: 368

View: 5599

A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.

Periods And Special Functions In Transcendence

Author: Tretkoff Paula B

Publisher: World Scientific

ISBN: 1786342960

Category: Mathematics

Page: 228

View: 3579

This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi–Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.

Eigenvalues, Multiplicities and Graphs

Author: Charles R. Johnson,Carlos M. Saiago

Publisher: Cambridge University Press

ISBN: 1108547036

Category: Mathematics

Page: N.A

View: 5235

The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.

Applications of Diophantine Approximation to Integral Points and Transcendence

Author: Pietro Corvaja,Umberto Zannier

Publisher: Cambridge University Press

ISBN: 1108656560

Category: Mathematics

Page: N.A

View: 5626

This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to Diophantine equations and related topics. The geometric viewpoint on Diophantine equations has been adopted throughout the book. It includes a number of results, some published here for the first time in book form, and some new, as well as classical material presented in an accessible way. Graduate students and experts alike will find the book's broad approach useful for their work, and will discover new techniques and open questions to guide their research. It contains concrete examples and many exercises (ranging from the relatively simple to the much more complex), making it ideal for self-study and enabling readers to quickly grasp the essential concepts.

Diophantine inequalities

Author: Roger Clive Baker

Publisher: Oxford University Press, USA


Category: Mathematics

Page: 275

View: 8234

This book launches the prestigious new series London Mathematical Society Monographs. The author, noted for his work throughout the mathematical community, here presents an overview of the theory of nonlinear Diophantine approximation. He has concentrated on the important progress made in the last ten years by such contributors as I. M. Vinogradov, H. Heilbronn, and W. M. Schmidt, finding, for example, that it is possible to consider simultaneous approximation to integers by values of a set of quadratic forms, or a discrete analogue (small solutions of a system of homogeneous congruences).

Zahlentheorie und Zahlenspiele

Sieben ausgewählte Themenstellungen

Author: Hartmut Menzer,Ingo Althöfer

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486989634

Category: Mathematics

Page: 336

View: 9995

This textbook presents the basic fundamentals of number theory along with more complex topics drawn from analytic and algebraic number theory. Each chapter includes a broad range of examples, study exercises with solutions, illustrations, and detailed presentations of proofs, making this book especially well-suited for examination preparation.

Einführung in Algebra und Zahlentheorie

Author: Rainer Schulze-Pillot

Publisher: Springer-Verlag

ISBN: 3642552161

Category: Mathematics

Page: 338

View: 8392

Das Buch bietet eine neue Stoffzusammenstellung, die elementare Themen aus der Algebra und der Zahlentheorie verknüpft und für die Verwendung in Bachelorstudiengängen und modularisierten Lehramtsstudiengängen konzipiert ist. Es führt die abstrakten Konzepte der Algebra in stetem Kontakt mit konkreten Problemen der elementaren Zahlentheorie und mit Blick auf Anwendungen ein und bietet Ausblicke auf fortgeschrittene Themen. In beiden Gebieten wird ein Stand erreicht, der für Nichtspezialisten das nötige Handwerkszeug für die meisten Anwendungen (etwa in diskreter Mathematik, Kryptographie oder Signalverarbeitung) vermittelt, aber auch zu einer vertieften Beschäftigung mit Algebra und Zahlentheorie anregt und für diese eine gute Ausgangsbasis bildet. Für die dritte Auflage wurden neben einer allgemeinen Überarbeitung und Fehlerkorrektur zahlreiche Beispiele und Aufgaben neu hinzugefügt. Ferner wird in einem neuen ergänzenden Abschnitt der Beweis der Sätze der linearen Algebra über Normalformen von Matrizen mit Hilfe des Elementarteilersatzes behandelt, da dieser schöne Beweis in Lehrbüchern der Linearen Algebra selten Platz findet.