purely periodic beta-expansions in the pisot non-unit case · purely periodic beta-expansions in...

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HAL Id: inria-00071966 https://hal.inria.fr/inria-00071966 Submitted on 23 May 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Purely Periodic beta-Expansions in the Pisot Non-unit Case Valerie Berthe, Anne Siegel To cite this version: Valerie Berthe, Anne Siegel. Purely Periodic beta-Expansions in the Pisot Non-unit Case. [Research Report] RR-4619, INRIA. 2002. inria-00071966

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Page 1: Purely Periodic beta-Expansions in the Pisot Non-unit Case · Purely Periodic beta-Expansions in the Pisot Non-unit Case Valerie Berthe, Anne Siegel To cite this version: Valerie

HAL Id: inria-00071966https://hal.inria.fr/inria-00071966

Submitted on 23 May 2006

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

Purely Periodic beta-Expansions in the Pisot Non-unitCase

Valerie Berthe, Anne Siegel

To cite this version:Valerie Berthe, Anne Siegel. Purely Periodic beta-Expansions in the Pisot Non-unit Case. [ResearchReport] RR-4619, INRIA. 2002. �inria-00071966�

Page 2: Purely Periodic beta-Expansions in the Pisot Non-unit Case · Purely Periodic beta-Expansions in the Pisot Non-unit Case Valerie Berthe, Anne Siegel To cite this version: Valerie

ISS

N 0

249-

6399

ISR

N IN

RIA

/RR

--46

19--

FR

+E

NG

ap por t de r ech er ch e

THÈME 3

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Purely Periodic beta-Expansionsin the Pisot Non-unit Case

Valérie Berthé — Anne Siegel

N° 4619

Novembre 2002

Page 3: Purely Periodic beta-Expansions in the Pisot Non-unit Case · Purely Periodic beta-Expansions in the Pisot Non-unit Case Valerie Berthe, Anne Siegel To cite this version: Valerie
Page 4: Purely Periodic beta-Expansions in the Pisot Non-unit Case · Purely Periodic beta-Expansions in the Pisot Non-unit Case Valerie Berthe, Anne Siegel To cite this version: Valerie

Unité de recherche INRIA RennesIRISA, Campus universitaire de Beaulieu, 35042 Rennes Cedex (France)

Téléphone : +33 2 99 84 71 00 — Télécopie : +33 2 99 84 71 71

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Page 5: Purely Periodic beta-Expansions in the Pisot Non-unit Case · Purely Periodic beta-Expansions in the Pisot Non-unit Case Valerie Berthe, Anne Siegel To cite this version: Valerie

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Page 7: Purely Periodic beta-Expansions in the Pisot Non-unit Case · Purely Periodic beta-Expansions in the Pisot Non-unit Case Valerie Berthe, Anne Siegel To cite this version: Valerie

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Unité de recherche INRIA RennesIRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot-St-Martin (France)Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)

ÉditeurINRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)��������� ���� ���������� ��� ���

ISSN 0249-6399