Diophantine Geometry

An Introduction

Author: Marc Hindry,Joseph H. Silverman

Publisher: Springer Science & Business Media

ISBN: 1461212103

Category: Mathematics

Page: 561

View: 8863

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This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Heights in Diophantine Geometry

Author: Enrico Bombieri,Walter Gubler

Publisher: Cambridge University Press

ISBN: 9780521712293

Category: Mathematics

Page: 652

View: 2613

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This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

Integral Points on Algebraic Varieties

An Introduction to Diophantine Geometry

Author: Pietro Corvaja

Publisher: Springer

ISBN: 9811026483

Category: Mathematics

Page: 75

View: 9973

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This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on algebraic varieties. This text rapidly introduces problems in Diophantine geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material. In some instances, proofs have been replaced by a detailed analysis of particular cases, referring to the quoted papers for complete proofs. A central role is played by Siegel’s finiteness theorem for integral points on curves. The book ends with the analysis of integral points on surfaces.

Diophantine geometry

proceedings

Author: Umberto Zannier

Publisher: Birkhauser

ISBN: 9788876422065

Category: Mathematics

Page: 390

View: 4236

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This book contains research articles on Diophantine Geometry, written by participants of a research program held at the Ennio De Giorgi Mathematical Research Center in Pisa, Italy, during the period April - July 2005. The authors are eminent experts in the field. Several subfields of the main topic are presented; the volume thus is particularly useful to get a broad overview of recent research developments.

PAMQ

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2232

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Number Theory for the Millennium III

Author: Michael A. Bennett

Publisher: A K Peters/CRC Press

ISBN: N.A

Category: Mathematics

Page: 470

View: 8892

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Building on the tradition of an outstanding series of conferences at the University of Illinois at Urbana-Champaign, the organizers attracted an international group of scholars to open the new Millennium with a conference that reviewed the current state of number theory research and pointed to future directions in the field. The conference was the largest general number theory conference in recent history, featuring a total of 159 talks, with the plenary lectures given by George Andrews, Jean Bourgain, Kevin Ford, Ron Graham, Andrew Granville, Roger Heath-Brown, Christopher Hooley, Winnie Li, Kumar Murty, Mel Nathanson, Ken Ono, Carl Pomerance, Bjorn Poonen, Wolfgang Schmidt, Chris Skinner, K. Soundararajan, Robert Tijdeman, Robert Vaughan, and Hugh Williams. The Proceedings Volumes of the conference review some of the major number theory achievements of this century and to chart some of the directions in which the subject will be heading during the new century. These volumes will serve as a useful reference to researchers in the area and an introduction to topics of current interest in number theory for a general audience in mathematics.

Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1643

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Model Theory : An Introduction

Author: David Marker

Publisher: Springer Science & Business Media

ISBN: 0387987606

Category: Mathematics

Page: 345

View: 1204

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Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures

Colloquium De Giorgi 2006

Author: Umberto Zannier

Publisher: Edizioni della Normale

ISBN: N.A

Category: Mathematics

Page: 57

View: 3720

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This book contains expositions of talks of the Colloquio De Giorgi, given by eminent experts and addressed to a ‘general’ public (audience) of mathematicians. The topics are prepared in such a way that readers will get some idea of recent progress in several mathematical fields.

Maß und Kategorie

Author: J.C. Oxtoby

Publisher: Springer-Verlag

ISBN: 364296074X

Category: Mathematics

Page: 112

View: 3252

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Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.

Elementary Geometry of Algebraic Curves

An Undergraduate Introduction

Author: C. G. Gibson

Publisher: Cambridge University Press

ISBN: 9780521646413

Category: Mathematics

Page: 250

View: 2212

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Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.

Automorphe Formen

Author: Anton Deitmar

Publisher: Springer-Verlag

ISBN: 3642123902

Category: Mathematics

Page: 252

View: 3487

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Das Buch bietet eine Einführung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen führt der Autor seine Leser hin zur modernen, darstellungstheoretischen Beschreibung von automorphen Formen und ihren L-Funktionen. Das Hauptgewicht legt er auf den Übergang von der klassischen, elementaren Sichtweise zu der modernen, durch die Darstellungstheorie begründete Herangehensweise. Diese Art der Verbindung von klassischer und moderner Sichtweise war in der Lehrbuchliteratur bisher nicht zu finden.

The 1-2-3 of Modular Forms

Lectures at a Summer School in Nordfjordeid, Norway

Author: Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier

Publisher: Springer Science & Business Media

ISBN: 9783540741190

Category: Mathematics

Page: 266

View: 3851

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This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.