Read e-book online Complex Multiplication (New Mathematical Monographs, 15) PDF

By Reinhard Schertz

ISBN-10: 0521766680

ISBN-13: 9780521766685

this can be a self-contained account of the cutting-edge in classical advanced multiplication that incorporates contemporary effects on earrings of integers and purposes to cryptography utilizing elliptic curves. the writer is exhaustive in his therapy, giving a radical improvement of the speculation of elliptic services, modular features and quadratic quantity fields and supplying a concise precis of the consequences from category box conception. the most effects are followed by way of numerical examples, equipping any reader with all of the instruments and formulation they want. issues lined contain: the development of sophistication fields over quadratic imaginary quantity fields via singular values of the modular invariant j and Weber's tau-function; particular development of earrings of integers in ray category fields and Galois module constitution; the development of cryptographically appropriate elliptic curves over finite fields; evidence of Berwick's congruences utilizing department values of the Weierstrass p-function; kinfolk among elliptic devices and sophistication numbers.

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Complex Multiplication (New Mathematical Monographs, 15) by Reinhard Schertz

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Categories: Number Theory