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# đ Elliptic Curves (MN-40) by Anthony W. Knapp â free download

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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:

Security code:

- 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:

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...

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 de...

Random matrix theory is an area of mathematics first developed by physicists interested in the energy levels of atomic nuclei, but it can also be used to describe some exotic phenomena in the number theory of elliptic curves. This book illustrates this in...

Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscur...

Contributors in mathematics, computer science, and engineering introduce students and other professionals in any of their fields to the theory and algorithms involved in elliptic and hyper-elliptic curve cryptology in great detail. The text contains very ...

The canonical strategy of modern mathematics when studying an object is to put this object into a collection, and see what properties they have in common. Most commonly, the objects depend on some parameter(s), and the goal is to find out how the objects ...

This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-SzegĂ¶ theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which sa...

This book introduces the theory of modular forms with an eye toward the Modularity Theorem:All rational elliptic curves arise from modular forms.The topics covered include* elliptic curves as complex tori and as algebraic curves,* modular curves as Rieman...

This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields...

The Third Edition of this standard reference work has grown to keep pace with our expanding knowledge of this vital subject, and will now consist of five volumes. Most chapters which appeared in the Second Edition have been revised. New chapters concern t...

The Second Edition of this popular textbook has benefited from several years of exposure to both teachers and students. Based on their own experiences as well as those of others, the authors have reorganized, added, and updated this work to meet the needs...

''Pigment-protein Complexes in Plastics - Synthesis and Assembly'' covers various aspects of the biosynthesis, assembly and function of plastid pigment-protein complexes. Its major focus is on chlorophyll-protein complexes which are addressed in relation ...