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#### Topology of Algebraic Curves

De Gruyter 2012; US$ 196.00The book summarizes the state and new results on the topology of trigonal curves in geometrically ruled surfaces. Emphasis is placed upon various applications of the theory to related areas, most notably singularplane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence of braid monodromy... more...

#### Geometric Modular Forms and Elliptic Curves

World Scientific Publishing Company 2011; US$ 164.00This 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 Shimura–Taniyama conjecture, is given. In addition, the book presents an outline of the proof... more...

#### The Arithmetic of Elliptic Curves

Springer 2009; US$ 59.95Treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. This book discusses the necessary algebro-geometric results, and offers an exposition of the geometry of elliptic curves, and the formal group of an elliptic curve. more...

#### Elliptic Curves

Taylor and Francis 2008; US$ 109.95Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of... more...

#### Introduction to Plane Algebraic Curves

Springer 2007; US$ 74.95This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their applications... more...

#### Ranks of Elliptic Curves and Random Matrix Theory

Cambridge University Press 2007; US$ 100.00This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices. more...

#### Handbook of Elliptic and Hyperelliptic Curve Cryptography

Taylor and Francis 2005; US$ 125.95The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller... more...

#### Heegner Points and Rankin L-Series

Cambridge University Press 2004; US$ 52.00Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments. more...

#### Elliptic Curves

De Gruyter 2003; US$ 147.00The 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 is to give an elementary introduction to elliptic curves. Since this branch of number theory is... more...

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