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＜電子ブック＞
An Introduction to Number Theory / by G. Everest, Thomas Ward
(Graduate Texts in Mathematics. ISSN:21975612 ; 232)

版	1st ed. 2005.
出版者	(London : Springer London : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	IX, 297 p : online resource
著者標目	*Everest, G author Ward, Thomas author SpringerLink (Online service)
件　名	LCSH:Number theory FREE:Number Theory
一般注記	A Brief History of Prime -- Diophantine Equations -- Quadratic Diophantine Equations -- Recovering the Fundamental Theorem of Arithmetic -- Elliptic Curves -- Elliptic Functions -- Heights -- The Riemann Zeta Function -- The Functional Equation of the Riemann Zeta Function -- Primes in an Arithmetic Progression -- Converging Streams -- Computational Number Theory An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject. In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory. A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography. Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to be introduced to some of the main themes in number theory HTTP:URL=https://doi.org/10.1007/b137432

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