Average Value Theorems in Function Fields

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


In Chapter 2 we touched upon the subject of average value theorems in A = F[T]. The technique which we used goes back to Carlitz who associated certain Dirichlet series with some of the basic number-theoretic functions and then expressed these Dirichlet series in terms of ζ A (s). The zeta function is so simple in the case of the polynomial ring that it was possible to arrive at very precise results for the average values in question. For example, for nA define d(n)to be the number of monic divisors of n.


Zeta Function Function Field Class Number Simple Pole Dirichlet Series 
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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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