Advertisement

Number Theory in Function Fields

  • Michael Rosen
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 210)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Michael Rosen
    Pages 1-9
  3. Michael Rosen
    Pages 23-31
  4. Michael Rosen
    Pages 63-76
  5. Michael Rosen
    Pages 101-113
  6. Michael Rosen
    Pages 149-167
  7. Michael Rosen
    Pages 193-217
  8. Michael Rosen
    Pages 219-239
  9. Michael Rosen
    Pages 257-281
  10. Michael Rosen
    Pages 305-327
  11. Back Matter
    Pages 329-361

About this book

Introduction

Elementary number theory is concerned with arithmetic properties of the ring of integers. 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, for example, analogues of the theorems of Fermat and Euler, Wilsons theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlets theorem on primes in an arithmetic progression. After presenting the required foundational material on function fields, the later chapters explore the analogy between global function fields and algebraic number fields. A variety of topics are presented, including: the ABC-conjecture, Artins conjecture on primitive roots, the Brumer-Stark conjecture, Drinfeld modules, class number formulae, and average value theorems.
The first few chapters of this book are accessible to advanced undergraduates. The later chapters are designed for graduate students and professionals in mathematics and related fields who want to learn more about the very fruitful relationship between number theory in algebraic number fields and algebraic function fields. In this book many paths are set forth for future learning and exploration.
Michael Rosen is Professor of Mathematics at Brown University, where hes been since 1962. He has published over 40 research papers and he is the co-author of A Classical Introduction to Modern Number Theory, with Kenneth Ireland. He received the Chauvenet Prize of the Mathematical Association of America in 1999 and the Philip J. Bray Teaching Award in 2001.

Keywords

Algebraic Function Fields Algebraic Geometry Function Fields Number theory Prime Prime number finite field

Authors and affiliations

  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-6046-0
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2954-9
  • Online ISBN 978-1-4757-6046-0
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking