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S-Units, S-Class Group, and the Corresponding L-Functions

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

Abstract

Let K/F be an algebraic function field over the field of constants F. Throughout this book we have been emphasizing the analogy between the arithmetic of K and that of an algebraic number field. This analogy is particulary clear when we choose an element xK which is not a constant. The ring A = F[x] ⊂ k = F(x) then plays the role of the pair ℤ ⊂ ℚ in number theory. K is an algebraic extension of F(x) and the analogue of the ring of integers in an algebraic number field is the integral closure of A in K. Let’s call this ring B. We will show that B is a Dedekind domain. We will investigate the unit group and the class group of B. We will also associate zeta and L-functions to B.

Keywords

Galois Group Function Field Class Number Integral Closure Effective Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

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

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