David A. Silverberg's Books

Arithmetic Algebraic Geometry

By: Brian David Conrad

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The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

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Page Count

588

Publisher

American Mathematical Soc.

ISBN 10

0821886916

ISBN 13

9780821886915

Some Problems of Unlikely Intersections in Arithmetic and Geometry

By: Umberto Zannier,David William Masser

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Some Problems of Unlikely Intersections in Arithmetic and Geometry

By: Umberto Zannier,David William Masser

This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the Andr -Oort conjecture (outlining work by Pila).

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176

Publisher

Princeton University Press

Published Date

ISBN 10

069115371X

ISBN 13

9780691153711

Séminaire de Théorie Des Nombres

Paris 1990-91

By: Sinnou David

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Séminaire de Théorie Des Nombres

Paris 1990-91

By: Sinnou David

Based on the lectures given at the Seminaire de Theorie des Nombres de Paris in 1990-1991, this collection of papers reflects work in many areas of number theory, including: cubic exponential sums; Riemann's period relations; and Galois representations attached to points on Shimura varieties.

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306

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817636846

ISBN 13

9780817636845

Algebraic Number Theory and Fermat's Last Theorem

By: Ian Stewart,David Tall

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Algebraic Number Theory and Fermat's Last Theorem

By: Ian Stewart,David Tall

Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work. New to the Fourth Edition Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(√14) is Euclidean Presents an important new result: Mihăilescu’s proof of the Catalan conjecture of 1844 Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last Theorem Improves and updates the index, figures, bibliography, further reading list, and historical remarks Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.

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338

Publisher

CRC Press

Published Date

ISBN 10

1498738400

ISBN 13

9781498738408

Public Key Infrastructure

Second European PKI Workshop: Research and Applications, EuroPKI 2005, Canterbury, UK, June 30- July 1, 2005, Revised Selected Papers

By: David Chadwick

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Public Key Infrastructure

Second European PKI Workshop: Research and Applications, EuroPKI 2005, Canterbury, UK, June 30- July 1, 2005, Revised Selected Papers

By: David Chadwick

This book constitutes the thoroughly refereed post-proceedings of the 2nd European Public Key Infrastructure Workshop: Research and Applications, EuroPKI 2005, held in Canterbury, UK, in June/July 2005. The 18 revised full papers presented were carefully reviewed and selected from 43 submissions. The papers are organized in topical sections on authorization, risks/attacks to PKI systems, interoperability between systems, evaluating a CA, ID ring based signatures, new protocols, practical implementations, and long term archiving.

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Page Count

281

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540280626

ISBN 13

9783540280620

Primes of the Form x2+ny2 : Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions

By: David A. Cox

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Primes of the Form x2+ny2 : Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions

By: David A. Cox

This book studies when a prime p can be written in the form x2+ny2. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of p=x2+ny2. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields. The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics.

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Page Count

551

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470470284

ISBN 13

9781470470289

Kernicterus

By: David W. McCandless

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Kernicterus

By: David W. McCandless

Kernicterus (bilirubin encephalopathy) is a highly interesting example of metabolic encephalopathy. It fills all the characteristics of a metabolic encephalopathy in that it can develop rapidly, produces signature signs and symptoms, and is amenable to successful treatment. In the absence of treatment kernicterus can produce devastating sequelae and death. The present volume will examine the biochemistry and physiology of bilirubin as well as its hepatic metabolism and renal excretion. Chapters will elaborate bodily disposition of bilirubin and its neuropathology. Both early treatments and current therapy will be discussed in detail. Phototherapy will be presented, and its efficacy and influence on incidence thoroughly examined.

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283

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441965556

ISBN 13

9781441965554

Primes of the Form x2+ny2

Fermat, Class Field Theory, and Complex Multiplication

By: David A. Cox

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Primes of the Form x2+ny2

Fermat, Class Field Theory, and Complex Multiplication

By: David A. Cox

An exciting approach to the history and mathematics of number theory “. . . the author’s style is totally lucid and very easy to read . . .the result is indeed a wonderful story.” —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat’s work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: • A well-motivated introduction to the classical formulation of class field theory • Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations • An elementary treatment of quadratic forms and genus theory • Simultaneous treatment of elementary and advanced aspects of number theory • New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.

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Page Count

418

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118400747

ISBN 13

9781118400746

Things Hunting Men

By: David Drake

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Things Hunting Men

By: David Drake

From the creator of Hammer's Slammers comes the second Starhunters volume. This time the tables are turned on the human killers. Now it is the monkey boys who are on the receiving end of the hunt. Includes stories by Gordon R. DIckson, Robert Silverberg, David Drak and others.

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Page Count

324

Published Date

ISBN 10

0671654128

ISBN 13

9780671654122

Book's by David A. Silverberg

Arithmetic Algebraic Geometry

Arithmetic Algebraic Geometry

Some Problems of Unlikely Intersections in Arithmetic and Geometry

Some Problems of Unlikely Intersections in Arithmetic and Geometry

Séminaire de Théorie Des Nombres

Séminaire de Théorie Des Nombres

Algebraic Number Theory and Fermat's Last Theorem

Algebraic Number Theory and Fermat's Last Theorem

Public Key Infrastructure

Public Key Infrastructure

Primes of the Form x2+ny2 : Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions

Primes of the Form x2+ny2 : Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions

Kernicterus

Kernicterus

Primes of the Form x2+ny2

Primes of the Form x2+ny2

Things Hunting Men

Things Hunting Men

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