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Sinossi
This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideles and adeles, and zeta functions. It also contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties. This version can now be seen as a precursor of Arakelov theory. Part II covers class field theory, and Part III is devoted to analytic methods, including an exposition of Tate's thesis, the Brauer-Siegel
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Recensione
Second Edition
S. Lang
Algebraic Number Theory
"This book is the second edition of Lang's famous and indispensable book on algebraic number theory. The major change from the previous edition is that the last chapter on explicit formulas has been completely rewritten. In addition, a few new sections have been added to the other chapters . . . Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."―MATHEMATICAL REVIEWS
Contenuti
One General Basic Theory.- I Algebraic Integers.- II Completions.- III The Different and Discriminant.- IV Cyclotomic Fields.- V Parallelotopes.- VI The Ideal Function.- VII Ideles and Adeles.- VIII Elementary Properties of the Zeta Function and L-series.- Two Class Field Theory.- IX Norm Index Computations.- X The Artin Symbol, Reciprocity Law, and Class Field Theory.- XI The Existence Theorem and Local Class Field Theory.- XII L-series Again.- Three Analytic Theory.- XIII Functional Equation of the Zeta Function, Hecke’s Proof.- XIV Functional Equation, Tate’s Thesis.- XV Density of Primes and Tauberian Theorem.- XVI The Brauer-Siegel Theorem.- XVII Explicit Formulas.
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This is a second edition of Lang s well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fiel. Codice articolo 4189556
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Algebraic Number Theory (Graduate Texts in Mathematics)
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Algebraic Number Theory
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms.'Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception.'--MATHEMATICAL REVIEWS 376 pp. Englisch. Codice articolo 9781461269229
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Algebraic Number Theory (Graduate Texts in Mathematics)
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Algebraic Number Theory
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Taschenbuch. Condizione: Neu. Neuware -The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which 1 make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collec tion of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of W eber, Hasse, Hecke, and Hilbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theo retically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre's book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, 1 have intermingled the ideal and idelic approaches without prejudice for either. 1 also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods).Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 376 pp. Englisch. Codice articolo 9781461269229
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which 1 make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collec tion of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of W eber, Hasse, Hecke, and Hilbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theo retically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre's book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, 1 have intermingled the ideal and idelic approaches without prejudice for either. 1 also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods). Codice articolo 9781461269229
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