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An effective criterion for periodicity of $ \ell$-adic continued fractions

Abstract:

The theory of continued fractions has been generalized to $ \ell $-adic numbers by several authors and presents many differences with respect to the real case. In the present paper we investigate the expansion of rationals and quadratic irrationals for the $ \ell $-adic continued fractions introduced by Ruban. In this case, rational numbers may have a periodic non-terminating continued fraction expansion; moreover, for quadratic irrational numbers, no analogue of Lagrange's theorem holds. We ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1090/mcom/3385

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More from this funder
Name:
Engineering and Physical Sciences Research Council
Funding agency for:
Capuano, L
Grant:
EP/N007956/1
More from this funder
Name:
INdAM
Funding agency for:
Capuano, L
Grant:
EP/N007956/1
More from this funder
Name:
European Research Council
Funding agency for:
Capuano, L
Grant:
EP/N007956/1
More from this funder
Name:
Centro di Ricerca Matematica “Ennio de Giorgi”
Funding agency for:
Veneziano, F
More from this funder
Name:
University of Basel
Funding agency for:
Veneziano, F
Publisher:
American Mathematical Society
Journal:
Mathematics of Computation More from this journal
Volume:
88
Issue:
318
Pages:
1851-1882
Publication date:
2018-10-18
Acceptance date:
2018-06-06
DOI:
EISSN:
1088-6842
ISSN:
0025-5718
Pubs id:
pubs:858835
UUID:
uuid:aba8e0a7-0c6e-44b0-ac2e-523fd2908f94
Local pid:
pubs:858835
Source identifiers:
858835
Deposit date:
2018-06-22

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