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MATHEMATICAL REVIEWS
"Both in the large (choice and arrangement of the material) and in the details (accuracy and completeness of proofs, quality of explanations and motivating remarks), the author did a marvelous job. His parallel treatment of topics...for both number and function fields demonstrates the strong interaction between the respective arithmetics, and allows for motivation on either side."
Bulletin of the AMS
"... Which brings us to the book by Michael Rosen. In it, one has an excellent (and, to the author's knowledge, unique) introduction to the global theory of function fields covering both the classical theory of Artin, Hasse, Weil and presenting an introduction to Drinfeld modules (in particular, the Carlitz module and its exponential). So the reader will find the basic material on function fields and their history (i.e., Weil differentials, the Riemann-Roch Theorem etc.) leading up to Bombieri's proof of the Riemann hypothesis first established by Weil. In addition one finds chapters on Artin's primitive root Conjecture for function fields, Brumer-Stark theory, the ABC Conjecture, results on class numbers and so on. Each chapter contains a list of illuminating exercises. Rosen's book is perfect for graduate students, as well as other mathematicians, fascinated by the amazing similarities between number fields and function fields."
David Goss (Ohio State University)
Reseña del editor
Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.
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- VerlagSpringer
- Erscheinungsdatum2010
- ISBN 10 1441929541
- ISBN 13 9781441929549
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten376
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Number Theory in Function Fields
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Paperback. Zustand: Very Good-. Zustand des Schutzumschlags: No Dust Jacket. Graduate Texts In Mathematics, 210; 9.0 X 6.0 X 0.8 inches; 369 pages. Bestandsnummer des Verkäufers 343333
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Number Theory in Function Fields (Graduate Texts in Mathematics)
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Number Theory in Function Fields
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Number Theory in Function Fields (Graduate Texts in Mathematics)
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Number Theory in Function Fields
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules. 376 pp. Englisch. Bestandsnummer des Verkäufers 9781441929549
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Number Theory in Function Fields
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Springer-Verlag New York Inc., 2010
ISBN 10: 1441929541
ISBN 13: 9781441929549
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Number Theory in Function Fields
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Springer New York, Springer US, 2010
ISBN 10: 1441929541
ISBN 13: 9781441929549
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con sidering finite algebraic extensions K of Q, which are called algebraic num ber fields, and investigating properties of the ring of algebraic integers OK C K, defined as the integral closure of Z in K. Bestandsnummer des Verkäufers 9781441929549
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Number Theory in Function Fields
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Number Theory in Function Fields
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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of vario. Bestandsnummer des Verkäufers 4173423
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Number Theory in Function Fields
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