Power Search
Low Price Guarantee
We Take School POs
Topics in the Theory of Algebraic Function Fields 2006 Edition
Contributor(s): Villa Salvador, Gabriel Daniel (Author)

View larger image

 ISBN: 0817644806     ISBN-13: 9780817644802
Publisher: Birkhauser
OUR PRICE: $123.49  

Binding Type: Hardcover - See All Available Formats & Editions
Published: July 2006
Qty:

Annotation: The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore the geometric-analytic aspects of function fields, but leaves an in-depth examination from this perspective to others.

Key topics and features:

* Contains an introductory chapter on algebraic and numerical antecedents, including transcendental extensions of fields, absolute values on Q, and Riemann surfaces

* Focuses on the RiemannRoch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more

* Includes chapters on extensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the RiemannHurwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, and Drinfeld modules

* Explains both the similarities and fundamental differences between function fields and number fields

* Includes many exercises and examples to enhance understanding and motivate further study

The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 1-4 can serve as the base of an introductory undergraduate course for mathematics majors, whilechapters 5-9 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions will also find the work an excellent reference.

Click for more in this series: Mathematics: Theory & Applications
Additional Information
BISAC Categories:
- Mathematics | Number Theory
- Mathematics | Geometry - Algebraic
- Mathematics | Algebra - General
Dewey: 512.3
LCCN: 2006927769
Series: Mathematics: Theory & Applications
Physical Information: 1.39" H x 6.66" W x 9.36" L (2.26 lbs) 652 pages
Features: Bibliography, Illustrated, Index
 
Descriptions, Reviews, Etc.
Publisher Description:

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.

 
Customer ReviewsSubmit your own review
 
To tell a friend about this book, you must Sign In First!