Abstract
The zeta function of a lattice over an order in a semisimpleQ-algebra introduced by L Solomon, is a generalization of Dedekind zeta function and has an Euler product in terms of local zeta functions. In this paper, the local zeta functions of localized orders in quadratic fields and hence the global ones are computed first by using Solomon's combinatorial method. Next the same formulae are obtained by considering orders in algebras (overp-adic fields) obtained by completing quadratic fields. In the complete case, the methods of integration initiated by Bushnell and Reiner to study Solomon's zeta functions are used.
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Saikia, P.K. Zeta functions of orders in quadratic fields. Proc. Indian Acad. Sci. (Math. Sci.) 98, 31–42 (1988). https://doi.org/10.1007/BF02880968
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DOI: https://doi.org/10.1007/BF02880968