**Author**: Gabriel Daniel Villa Salvador

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817645151

**Category:** Mathematics

**Page:** 652

**View:** 586

**Author**: Gabriel Daniel Villa Salvador

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817645151

**Category:** Mathematics

**Page:** 652

**View:** 586

Language: en

Pages: 652

Pages: 652

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

Language: en

Pages: 260

Pages: 260

This book has two objectives. The first is to fill a void in the existing mathematical literature by providing a modern, self-contained and in-depth exposition of the theory of algebraic function fields. Topics include the Riemann-Roch theorem, algebraic extensions of function fields, ramifications theory and differentials. Particular emphasis is placed

Language: en

Pages: 358

Pages: 358

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

Language: en

Pages: 165

Pages: 165

This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along

Language: en

Pages: 201

Pages: 201

The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new