Introduction to Modern Number Theory
Publication year: 2005
ISBN: 978-3-540-27692-0
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"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
Subject: Mathematics and Statistics, Arithmetic, Arithmetic der algebraischen Zahlen, Elementare Zahlentheorie, Elementary number theory, Langlands program, Langlands-Programm, algebraic varieties, arithmetic of algebraic numbers, commutative property, diophantine equations, diophantische Gleichungen, elliptic curves, elliptische Kurven, number theory, public
