Diophantine Analysis - Steuding, Jorn

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Résumé :
Diophantine analysis is an extremely active field in number theory because of its many open problems and conjectures. Requiring only a basic understanding of number theory, Diophantine Analysis is built around the detailed theory of continued fractions and features many applications and examples. The author includes many new topics related to discrete mathematics, such as factoring large integers, error-free computing, and factoring polynomials. He also provides problem sections at the end of each chapter, where open problems are discussed along with other new topics, such as Apery's proof of irrationality, the polynomial Pell equation, and the abc-conjecture.

Sommaire:
Introduction: basic principles. Classical approximation theorems. Continued fractions. The irrationality of zeta(3). Quadratic irrationals. The Pell equation. Factoring with continued fractions. Transcendental numbers. The theorem of Roth. The abc-conjecture. P-adic numbers. Hensel's lemma. The local-global principle.