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Zeta functions of representations. (English) Zbl 1352.11081

Summary: Special functions have been played an important role in representation theory. Among others, we look at zeta functions attached to representations of groups. The zeta functions for the abelian groups \(\mathbb R^r\) introduced here are of new kind. Our purpose is to indicate a representation theoretic way to absolute zeta functions extending the previous paper [the authors, Proc. Japan Acad., Ser. A 89, No. 7, 75–79 (2013; Zbl 1373.11063)].

MSC:

11M32 Multiple Dirichlet series and zeta functions and multizeta values
11M35 Hurwitz and Lerch zeta functions
11M06 \(\zeta (s)\) and \(L(s, \chi)\)

Citations:

Zbl 1373.11063
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