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Cover: 9780387979663 | Introduction to Elliptic Curves and Modular Forms | Neal I. Koblitz
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Introduction to Elliptic Curves and Modular Forms
Buch von Neal I. Koblitz
Sprache: Englisch

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Beschreibung
This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses. thereby solidifying their under­ standing of some basic tools used throughout mathematics. Graduate stu­ dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under­ graduates could use the book for independent study projects, senior theses, and seminar work.
This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses. thereby solidifying their under­ standing of some basic tools used throughout mathematics. Graduate stu­ dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under­ graduates could use the book for independent study projects, senior theses, and seminar work.
Zusammenfassung
The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer.
Inhaltsverzeichnis
1 From Congruent Numbers to Elliptic Curves.- II The Hasse-Weil L-Function of an Elliptic Curve.- III Modular forms.- IV Modular Forms of Half Integer Weight.- Answers, Hints, and References for Selected Exercises.
Details
Erscheinungsjahr: 1993
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: x
252 S.
ISBN-13: 9780387979663
ISBN-10: 0387979662
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Koblitz, Neal I.
Auflage: 2nd ed. 1993
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 20 mm
Von/Mit: Neal I. Koblitz
Erscheinungsdatum: 29.04.1993
Gewicht: 0,571 kg
Artikel-ID: 102424795
Zusammenfassung
The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer.
Inhaltsverzeichnis
1 From Congruent Numbers to Elliptic Curves.- II The Hasse-Weil L-Function of an Elliptic Curve.- III Modular forms.- IV Modular Forms of Half Integer Weight.- Answers, Hints, and References for Selected Exercises.
Details
Erscheinungsjahr: 1993
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: x
252 S.
ISBN-13: 9780387979663
ISBN-10: 0387979662
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Koblitz, Neal I.
Auflage: 2nd ed. 1993
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 20 mm
Von/Mit: Neal I. Koblitz
Erscheinungsdatum: 29.04.1993
Gewicht: 0,571 kg
Artikel-ID: 102424795
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