Abstract
In this section we will introduce Γ-functions into the arithmetic of function fields. We do this by building on a basic, and still quite mysterious, construction of L. Carlitz in the A = F r [T]-case. Recall that in Section 3.3 we introduced the Carlitz exponential
where \({D_0} = 1,{D_j} = \left[ j \right]{\left[ {j - 1} \right]^r} \cdots {\left[ 1 \right]^{{r^{j - 1}}}},\) for j > 1, and \(\left[ j \right] = {T^{{r^j}}} - T \). In Proposition 3.1.6 we showed that
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© 1998 Springer-Verlag Berlin Heidelberg
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Goss, D. (1998). Γ-functions. In: Basic Structures of Function Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebeite. 3. Folge, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61480-4_9
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DOI: https://doi.org/10.1007/978-3-642-61480-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63541-3
Online ISBN: 978-3-642-61480-4
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