Generalized \(t\)-modules
The notions of Drinfeld module, \(t\)-module, etc., are ``classically'' based on the \(q\)th power mapping in characteristic \(p\). It has been known for quite a while that much of the theory can be developed in the more abstract situation of an arbitrary field equipped with a field automorphism of infinite order. In fact, one can more generally replace the \(q\)th power mapping with a continuous \(F\)-endomorphism of the field \(F((1/\theta))\); for instance, \(\theta\mapsto\theta^d\), \(d\geq 2\). The first author has previously presented a very interesting theory of such ``generalized Drinfeld modules'' [see, e.g., Galois calculus and Carlitz exponentials, in: The arithmetic of function fields (eds: D. Goss et al) de Gruyter, 33-50 (1992; Zbl 0794.11025)], and the present work is a continuation of this study. The authors introduce a tensor product into the theory based on the one previously defined by \textit{G. Anderson} in the ``classical'' theory of Drinfeld modules [Duke Math. J. 53, 457-502 (1986; Zbl 0679.14001)]. The authors then apply this theory to certain zeta-values following \textit{G. Anderson} and \textit{D. Thakur} [Ann. Math., II. Ser. 132, 159-191 (1990; Zbl 0713.11082)].
scientific article; zbMATH DE number 1014014
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