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Cover: 9780387849225 | Solving the Pell Equation | Hugh Williams (u. a.) | Buch | XX | 2008
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Solving the Pell Equation
Buch von Hugh Williams (u. a.)
Sprache: Englisch

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Beschreibung
Pell¿s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell¿s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation.

The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell¿s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.
Pell¿s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell¿s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation.

The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell¿s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.
Zusammenfassung

Describes modern (and surprising) applications to cryptography

Includes the most recent advances, with a deeper approach than any other book

Hugh Williams is Canada's most famous computational number theorist who has published close to 200 articles in top journals

Michael Jacobson is the known expert on subexponential methods, and a former student of Hugh Williams

Both authors are known as outstanding expositors

Includes supplementary material: [...]

Inhaltsverzeichnis
Early History of the Pell Equation.- Continued Fractions.- Quadratic Number Fields.- Ideals and Continued Fractions.- Some Special Pell Equations.- The Ideal Class Group.- The Analytic Class Number Formula.- Some Additional Analytic Results.- Some Computational Techniques.- (f, p) Representations of -ideals.- Compact Representations.- The Subexponential Method.- Applications to Cryptography.- Unconditional Verification of the Regulator and the Class Number.- Principal Ideal Testing in .- Conclusion.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: CMS Books in Mathematics
Inhalt: xx
495 S.
ISBN-13: 9780387849225
ISBN-10: 038784922X
Sprache: Englisch
Herstellernummer: 11775560
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Williams, Hugh
Jacobson, Michael
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
CMS Books in Mathematics
Maße: 241 x 160 x 34 mm
Von/Mit: Hugh Williams (u. a.)
Erscheinungsdatum: 02.12.2008
Gewicht: 0,934 kg
Artikel-ID: 101734930
Zusammenfassung

Describes modern (and surprising) applications to cryptography

Includes the most recent advances, with a deeper approach than any other book

Hugh Williams is Canada's most famous computational number theorist who has published close to 200 articles in top journals

Michael Jacobson is the known expert on subexponential methods, and a former student of Hugh Williams

Both authors are known as outstanding expositors

Includes supplementary material: [...]

Inhaltsverzeichnis
Early History of the Pell Equation.- Continued Fractions.- Quadratic Number Fields.- Ideals and Continued Fractions.- Some Special Pell Equations.- The Ideal Class Group.- The Analytic Class Number Formula.- Some Additional Analytic Results.- Some Computational Techniques.- (f, p) Representations of -ideals.- Compact Representations.- The Subexponential Method.- Applications to Cryptography.- Unconditional Verification of the Regulator and the Class Number.- Principal Ideal Testing in .- Conclusion.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: CMS Books in Mathematics
Inhalt: xx
495 S.
ISBN-13: 9780387849225
ISBN-10: 038784922X
Sprache: Englisch
Herstellernummer: 11775560
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Williams, Hugh
Jacobson, Michael
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
CMS Books in Mathematics
Maße: 241 x 160 x 34 mm
Von/Mit: Hugh Williams (u. a.)
Erscheinungsdatum: 02.12.2008
Gewicht: 0,934 kg
Artikel-ID: 101734930
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