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# ðŸ“™ Elliptic Curves (MN-40) by Anthony W. Knapp â€” free download

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**Elliptic Curves. (MN-40) free epub by Anthony W. Knapp**

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--ellip...

**Elliptic Curves. (MN-40) epub download by Anthony W. Knapp**

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--ellip...

**Testing primality using elliptic curves pdf free by Goldwasser.**

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An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects - elliptic curves and modular forms - come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem.Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics - including class field theory, arithmetic algebraic geometry, and group representations - in which the concidence of L functions relates analysis and algebra in the most fundamental ways.Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner.

## About book:

## About file:

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- Series:
**MN-40** - Author:
**Anthony W. Knapp** - Year:
**1992** - Publisher:
**Princeton University Press** - Language:
**English** - ISBN:
**9780691085593,0691085595**

- File size:
**25 561 898** - Format:
**djvu**

Security code:

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--ellip...

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--ellip...

We present a primality proving algorithm-a probablistic primality test that produces short certificates of primality on prime inputs. We prove that the test runs in expected polynomial time for all but a vanishingly small fraction of the primes. As a coro...

Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tat...

The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contempo...

The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory.The purpose of the present textbook ...

Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the co...

This book surveys some recent developments in the arithmetic of modular elliptic curves. It places special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modular...

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimur...