Number systems over orders

A. Pethő, Jörg Thuswaldner

Research output: Article

2 Citations (Scopus)

Abstract

Let (Formula presented.) be a number field of degree k and let (Formula presented.) be an order in (Formula presented.). A generalized number system over(Formula presented.) (GNS for short) is a pair (Formula presented.) where (Formula presented.) is monic and (Formula presented.) is a complete residue system modulo p(0) containing 0. If each (Formula presented.) admits a representation of the form (Formula presented.) with (Formula presented.) and (Formula presented.) then the GNS (Formula presented.) is said to have the finiteness property. To a given fundamental domain (Formula presented.) of the action of (Formula presented.) on (Formula presented.) we associate a class (Formula presented.) of GNS whose digit sets (Formula presented.) are defined in terms of (Formula presented.) in a natural way. We are able to prove general results on the finiteness property of GNS in (Formula presented.) by giving an abstract version of the well-known “dominant condition” on the absolute coefficient p(0) of p. In particular, depending on mild conditions on the topology of (Formula presented.) we characterize the finiteness property of (Formula presented.) for fixed p and large (Formula presented.). Using our new theory, we are able to give general results on the connection between power integral bases of number fields and GNS.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalMonatshefte fur Mathematik
DOIs
Publication statusAccepted/In press - máj. 18 2018

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Number system
Finiteness
Number field

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Number systems over orders. / Pethő, A.; Thuswaldner, Jörg.

In: Monatshefte fur Mathematik, 18.05.2018, p. 1-24.

Research output: Article

Pethő, A. ; Thuswaldner, Jörg. / Number systems over orders. In: Monatshefte fur Mathematik. 2018 ; pp. 1-24.
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