Number systems over orders

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901XYX" target="_blank" >RIV/61988987:17310/18:A1901XYX - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00605-018-1191-x" target="_blank" >http://dx.doi.org/10.1007/s00605-018-1191-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00605-018-1191-x" target="_blank" >10.1007/s00605-018-1191-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Number systems over orders

Popis výsledku v původním jazyce

LetKbe a number field of degree k and letObe an order inK. Ageneralized number system over O GNS for short) is a pair p, D) where p. O[x] is monic and D. O is a complete residue system modulo p0) containing 0. If each a. O[x] admits a representation of the form a = - 1 j= 0 dj x j mod p) with . N and d0,..., d - 1. D then the GNS p, D) is said to have the finiteness property. To a given fundamental domain F of the action of Zk on Rk we associate a class GF := {p, DF) : p. O[x]} of GNS whose digit sets DF are defined in terms of F in a natural way. We are able to prove general results on the finiteness property of GNS in GF by giving an abstract version of the well- known " dominant condition" on the absolute coefficient p0) of p. In particular, depending on mild conditions on the topology of F we characterize the finiteness property of px +/- m), DF) for fixed p and large m. N. Using our new theory, we are able to give general results on the connection between power integral bases of number fields and GNS.

Název v anglickém jazyce

Number systems over orders

Popis výsledku anglicky

LetKbe a number field of degree k and letObe an order inK. Ageneralized number system over O GNS for short) is a pair p, D) where p. O[x] is monic and D. O is a complete residue system modulo p0) containing 0. If each a. O[x] admits a representation of the form a = - 1 j= 0 dj x j mod p) with . N and d0,..., d - 1. D then the GNS p, D) is said to have the finiteness property. To a given fundamental domain F of the action of Zk on Rk we associate a class GF := {p, DF) : p. O[x]} of GNS whose digit sets DF are defined in terms of F in a natural way. We are able to prove general results on the finiteness property of GNS in GF by giving an abstract version of the well- known " dominant condition" on the absolute coefficient p0) of p. In particular, depending on mild conditions on the topology of F we characterize the finiteness property of px +/- m), DF) for fixed p and large m. N. Using our new theory, we are able to give general results on the connection between power integral bases of number fields and GNS.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

MONATSH MATH

ISSN

0026-9255

e-ISSN

1436-5081

Svazek periodika

187

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

24

Strana od-do

681-704

Kód UT WoS článku

000446558400006

EID výsledku v databázi Scopus

2-s2.0-85047154745