Average Value Theorems in Function Fields
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 n ∈ A define d(n)to be the number of monic divisors of n.
KeywordsZeta Function Function Field Class Number Simple Pole Dirichlet Series
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