Continued fractions in local fields, II
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- by Jerzy Browkin;
- Math. Comp. 70 (2001), 1281-1292
- DOI: https://doi.org/10.1090/S0025-5718-00-01296-5
- Published electronically: October 18, 2000
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Abstract:
The present paper is a continuation of an earlier work by the author. We propose some new definitions of $p$-adic continued fractions. At the end of the paper we give numerical examples illustrating these definitions. It turns out that for every $m,$ $1<m<5000,\ 5\nmid m$ if $\sqrt {m}\in \mathbb {Q} _{5}\setminus \mathbb {Q},$ then $\sqrt {m}$ has a periodic continued fraction expansion. The same is not true in $\mathbb {Q}_{p}$ for some larger values of $p.$References
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Bibliographic Information
- Jerzy Browkin
- Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL–02–097 Warsaw, Poland
- Email: bro@mimuw.edu.pl
- Received by editor(s): August 25, 1999
- Published electronically: October 18, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 1281-1292
- MSC (2000): Primary 11J70; Secondary 11S85
- DOI: https://doi.org/10.1090/S0025-5718-00-01296-5
- MathSciNet review: 1826582