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Geometric and Analytic Number Theory

Author: Edmund Hlawka

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 247

ISBN-13: 364275306X

In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H. Lenstraj furthermore, tried and tested examples and exercises have been included. The translator, Prof. Charles Thomas, has solved the difficult problem of the German text into English in an admirable way. He deserves transferring our 'Unreserved praise and special thailks. Finally, we would like to express our gratitude to Springer-Verlag, for their commitment to the publication of this English edition, and for the special care taken in its production. Vienna, March 1991 E. Hlawka J. SchoiBengeier R. Taschner Preface to the German Edition We have set ourselves two aims with the present book on number theory. On the one hand for a reader who has studied elementary number theory, and who has knowledge of analytic geometry, differential and integral calculus, together with the elements of complex variable theory, we wish to introduce basic results from the areas of the geometry of numbers, diophantine ap proximation, prime number theory, and the asymptotic calculation of number theoretic functions. However on the other hand for the student who has al ready studied analytic number theory, we also present results and principles of proof, which until now have barely if at all appeared in text books.

Noncommutative Geometry and Number Theory

Author: Caterina Consani

Publisher: Springer Science & Business Media

Published: 2007-12-18

Total Pages: 374

ISBN-13: 3834803529

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In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Number Theory and Algebraic Geometry

Author: Miles Reid

Publisher: Cambridge University Press

Published: 2003

Total Pages: 312

ISBN-13: 9780521545181

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This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.

The Geometry of Numbers

Author: C. D. Olds

Publisher: Cambridge University Press

Published: 2001-02-22

Total Pages: 198

ISBN-13: 9780883856437

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A self-contained introduction to the geometry of numbers.

Analytic Number Theory

Author: J. B. Friedlander

Publisher: Springer

Published: 2006-09-15

Total Pages: 217

ISBN-13: 9783540363637

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The four papers collected in this book discuss advanced results in analytic number theory, including recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials; counting integer solutions to Diophantine equations, using results from algebraic geometry and the geometry of numbers; the theory of Siegel’s zeros and of exceptional characters of L-functions; and an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg.

Contributions in Analytic and Algebraic Number Theory

Author: Valentin Blomer

Publisher: Springer Science & Business Media

Published: 2011-11-19

Total Pages: 301

ISBN-13: 1461412196

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The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson", held at the University Göttingen, July 27-29 2009. Many of the included chapters have been contributed by invited participants. This volume presents and investigates the most recent developments in various key topics in analytic number theory and several related areas of mathematics. The volume is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.

Algebraic Curves and Riemann Surfaces

Author: Rick Miranda

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 414

ISBN-13: 0821802682

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In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

Introduction to Analytic Number Theory

Author: Tom M. Apostol

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 352

ISBN-13: 1475755791

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"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS

Geometric and Analytic Number Theory

Author: Edmund Hlawka

Publisher:

Published: 1991-08-02

Total Pages: 252

ISBN-13: 9783642753077

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Local Analytic Geometry

Author: Theo de Jong

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 395

ISBN-13: 3322901599

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Auf der Grundlage einer Einführung in die kommutative Algebra, algebraische Geometrie und komplexe Analysis werden zunächst Kurvensingularitäten untersucht. Daran schließen Ergebnisse an, die zum ersten Mal in einem Lehrbuch aufgenommen wurden, das Verhalten von Invarianten in Familien, Standardbasen für konvergente Potenzreihenringe, Approximationssätze, Grauerts Satz über die Existenz der versellen Deformation. Das Buch richtet sich an Studenten höherer Semester, Doktoranden und Dozenten. Es ist auf der Grundlage mehrerer Vorlesungen und Seminaren an den Universitäten in Kaiserslautern und Saarbrücken entstanden.