The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. 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. This new edition details the current state of knowledge of elliptic curves.
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10 of 12 people found the following review helpful:
5.0 out of 5 stars
Clearly the best,
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This review is from: Introduction to Elliptic Curves and Modular Forms (Graduate Texts in Mathematics) (Hardcover)
This is not an easy book---it's certainly intended for graduate students---but it's also clearly the best introduction to the mathematics that give rise to the Taniyama-Shimura conjecture and the ideas that underlie the Wiles proof of Fermat's Last Theorem, and as such it deserves a prominent place in the world's intellectual life. And you have to love a math text that has a beautiful frontispiece (a sketch by Fomenko whose mathematical meaning I am still trying to work out).
4 of 4 people found the following review helpful:
5.0 out of 5 stars
Brilliant Exposition,
By Julius Vernon "J Vernon" (Manassas, VA) - See all my reviews
This review is from: Introduction to Elliptic Curves and Modular Forms (Graduate Texts in Mathematics) (Hardcover)
Koblitz is in his element with this text. Much like Daniel Marcus's Number Fields, Koblitz develops a ground work to begin the study of elliptic curves. Here he builds upon the ancient problem of congruent numbers to help develop motivation for an in depth study of elliptic curves and modular forms. Not for the faint of (mathematical) heart, but a truly brilliant piece added to the number theoretic literature. A must own for those interested in advanced ideas behind elliptic curves.
8 of 11 people found the following review helpful:
5.0 out of 5 stars
Organized and Wonderful,
By Alan Wong (Markham, Ontario, Canada) - See all my reviews
This review is from: Introduction to Elliptic Curves and Modular Forms (Graduate Texts in Mathematics) (Hardcover)
The book provides an excellent and readable introduction to elliptic curves, using the complex analysis approach. It gives detailed proof to many theorems, and the exercises for each chapter are wonderful. It is a good supplement for those who use another book by Koblitz: Algebraic Aspects of Cryptography (AAC). It is funny that Koblitz has copied and pasted some of the paragraphs from Introduction to Elliptic Curves and Modular Forms to AAC!
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Inside This Book
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First Sentence:
The theory of elliptic curves and modular forms is one subject where the most diverse branches of mathematics come together: complex analysis, algebraic geometry, representation theory, number theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
congruent number problem, half integer weight, modular points, congruent numbers, right triangle with rational sides, normalized eigenforms, automorphy factor, half integral weight, cusp condition, elliptic curve, fundamental parallelogram, cusp form, congruence subgroup, formes modulaires, nontrivial character, modular forms, critical strip, prime congruent, quadratic character, pure weight, fundamental domain, double cosets, modular function, double periodicity, coset representatives Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hasse-Weil L-function, Hecke L-series, Dirichlet L-series New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The theory of elliptic curves and modular forms is one subject where the most diverse branches of mathematics come together: complex analysis, algebraic geometry, representation theory, number theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
congruent number problem, half integer weight, modular points, congruent numbers, right triangle with rational sides, normalized eigenforms, automorphy factor, half integral weight, cusp condition, elliptic curve, fundamental parallelogram, cusp form, congruence subgroup, formes modulaires, nontrivial character, modular forms, critical strip, prime congruent, quadratic character, pure weight, fundamental domain, double cosets, modular function, double periodicity, coset representatives Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hasse-Weil L-function, Hecke L-series, Dirichlet L-series New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
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- A Course in Arithmetic (Graduate Texts in Mathematics) by Jean Pierre Serre on 4 pages
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), Back Matter (2), and Back Matter (3)
- Algebraic Number Theory (Advanced Studies in Pure Mathematics) by John Coates in Back Matter (1), and Back Matter (2)
- Lectures on the Theory of Algebraic Numbers (Graduate Texts in Mathematics) by E. T. Hecke in Back Matter (1), and Back Matter (2)
- An Introduction to Algebraic Topology (Graduate Texts in Mathematics) by Joseph J. Rotman in Back Matter (1), and Back Matter (2)
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- Elliptic Curves (Graduate Texts in Mathematics) by Dale Husemöller in Back Matter (1), Back Matter (2), and Back Matter (3)
- Software Process Technology: 5th European Workshop, EWSPT '96, Nancy, France, October 9 - 11, 1996. Proceedings (Lecture Notes in Computer Science) by Carlo Montangero on page 31, and page 346
- Glimpses of Algebra and Geometry by Gabor Toth on page 44, and page 196
- From Number Theory to Physics by Michel Waldschmidt on page 237, and page 289
- An Introduction to the Theory of Numbers by Ivan Niven in Back Matter
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