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Cover: 9781441929549 | Number Theory in Function Fields | Michael Rosen | Taschenbuch | xi
Rückseite: 9781441929549 | Number Theory in Function Fields | Michael Rosen | Taschenbuch | xi
Cover: 9781441929549 | Number Theory in Function Fields | Michael Rosen | Taschenbuch | xi
Rückseite: 9781441929549 | Number Theory in Function Fields | Michael Rosen | Taschenbuch | xi
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Number Theory in Function Fields
Taschenbuch von Michael Rosen
Sprache: Englisch

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Beschreibung
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."
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."
Zusammenfassung
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."
Inhaltsverzeichnis
* Polynomials over Finite Fields * Primes, Arithmetic Functions, and the Zeta Function * The Reciprocity Law * Dirichlet L-series and Primes in an Arithmetic Progression * Algebraic Function Fields and Global Function Fields * Weil Differentials and the Canonical Class * Extensions of Function Fields, Riemann-Hurwitz, and the ABC Theorem * Constant Field Extensions * Galois Extensions - Artin and Hecke L-functions * Artin's Primitive Root Conjecture * The Behavior of the Class Group in Constant Field Extensions * Cyclotomic Function Fields * Drinfeld Modules, An Introduction * S-Units, S-Class Group, and the Corresponding L-functions * The Brumer-Stark Conjecture * Class Number Formulas in Quadratic and Cyclotomic Function Fields * Average Value Theorems in Function Fields
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xi
358 S.
ISBN-13: 9781441929549
ISBN-10: 1441929541
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Rosen, Michael
Hersteller: Springer
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 21 mm
Von/Mit: Michael Rosen
Erscheinungsdatum: 03.12.2010
Gewicht: 0,569 kg
Artikel-ID: 107252983
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