Topics in the theory of algebraic function fields
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The work Topics in the theory of algebraic function fields represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Topics in the theory of algebraic function fields
Resource Information
The work Topics in the theory of algebraic function fields represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Topics in the theory of algebraic function fields
 Statement of responsibility
 Gabriel Daniel Villa Salvador
 Language

 eng
 spa
 eng
 Summary
 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 arithmeticalgebraic 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 geometricanalytic aspects of function fields, but leaves an indepth 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 14 can serve as the base of an introductory undergraduate course for mathematics majors, while chapters 59 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
 Cataloging source
 GW5XE
 Dewey number
 515.9
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA341
 LC item number
 .V5513 2006eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Mathematics: Theory & Applications
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