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Synopsis
This book studies the relationship between number theory in algebraic number fields and algebraic function fields. Because function fields are a bit different from number fields, even the experienced number theorist will learn from this book. Algebraic geometers will like the book, since the geometry of curves over an algebraically closed field is both pretty and elementary. Michael Rosen is the author of the successful book "A Classical Introduction to Modern Number Theory." He is the recipient of the 1999 Chauvenet Prize for his article "Niels Hendrik Abel and Equations of the Fifth Degree."
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Number Theory in Function Fields
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Springer New York, 2010
ISBN 10 : 1441929541
ISBN 13 : 9781441929549
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Etat : 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. N° de réf. du vendeur 4173423
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Number Theory in Function Fields
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Springer New York Dez 2010, 2010
ISBN 10 : 1441929541
ISBN 13 : 9781441929549
Neuf
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Taschenbuch. Etat : 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. N° de réf. du vendeur 9781441929549
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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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PF. Etat : New. N° de réf. du vendeur 6666-IUK-9781441929549
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Number Theory in Function Fields
Edité par
Springer New York, Springer US Dez 2010, 2010
ISBN 10 : 1441929541
ISBN 13 : 9781441929549
Neuf
Taschenbuch
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Taschenbuch. Etat : Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 376 pp. Englisch. N° de réf. du vendeur 9781441929549
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Number Theory in Function Fields
Edité par
Springer New York, Springer US, 2010
ISBN 10 : 1441929541
ISBN 13 : 9781441929549
Neuf
Taschenbuch
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Taschenbuch. Etat : 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. N° de réf. du vendeur 9781441929549
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Number Theory in Function Fields
Edité par
Springer, 2010
ISBN 10 : 1441929541
ISBN 13 : 9781441929549
Ancien ou d'occasion
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Paperback. Etat : Very Good-. Etat de la jaquette : No Dust Jacket. Graduate Texts In Mathematics, 210; 9.0 X 6.0 X 0.8 inches; 369 pages. N° de réf. du vendeur 343333
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Number Theory in Function Fields
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Number Theory in Function Fields
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Number Theory in Function Fields
Edité par
Springer-Verlag New York Inc., 2010
ISBN 10 : 1441929541
ISBN 13 : 9781441929549
Neuf
Paperback / softback
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Paperback / softback. Etat : New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 557. N° de réf. du vendeur C9781441929549
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