Zeta functions of orders in quadratic fields
type: Item
instance of: scholarly article
title: Zeta functions of orders in quadratic fields
zbMATH Open document ID: 0687.12007
DOI: 10.1007/BF02880968
author: P. K. Saikia
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1988-01-01T00:00:00Z
review text: \textit{L. Solomon} [Adv. Math. 26, 306-326 (1977; Zbl 0374.20007); Proc. Symp. Pure Math. 34, 309-329 (1979; Zbl 0432.05006)] has introduced the zeta-function of a lattice over an order in a semisimple \({\mathbb{Q}}\)- algebra as generalization of Dedekind's zeta-function. With the help of p-adic integration some problems connected with these zeta functions were studied by \textit{C. J. Bushnell} and \textit{I. Reiner} [Math. Z. 173, 135- 161 (1980; Zbl 0438.12004); J. Reine Angew. Math. 327, 156-183 (1981; Zbl 0455.12010)]. The author computes the local zeta-function of localized orders in quadratic fields (and hence the global ones) by Solomon's combinatorial method. There are also applications of Bushnell-Reiner's methods to some local zeta-functions.
Mathematics Subject Classification ID: 11R52
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11S40
zbMATH DE Number: 4125505
MaRDI profile type: Publication
cites work: Q5731856
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cites work: Q3922829
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full work available at URL: https://doi.org/10.1007/bf02880968
OpenAlex ID: W2092483742
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description: scientific article; zbMATH DE number 4125505