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Zeta functions of certain noncommutative algebras. (English) Zbl 1250.11087

From the text: For a fixed prime \(l\in\mathbb Z\), we consider zeta functions for certain types of (not necessarily commutative) algebras over the completion \(\mathbb Q_l\) of \(\mathbb Q\) and show that they satisfy several properties analogous to those of the usual Hasse-Weil zeta function of an algebraic variety over a finite field. Further, we develop appropriate functional equations for these zeta functions and also verify that they are rational functions over \(\mathbb Q_l\). We also extend classical results such as the Lefschetz fixed point formula to this context.

MSC:

11M38 Zeta and \(L\)-functions in characteristic \(p\)
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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References:

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