Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Continued fractions in local fields, II


Author: Jerzy Browkin
Journal: Math. Comp. 70 (2001), 1281-1292
MSC (2000): Primary 11J70; Secondary 11S85
Published electronically: October 18, 2000
MathSciNet review: 1826582
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11J70, 11S85

Retrieve articles in all journals with MSC (2000): 11J70, 11S85


Additional Information

Jerzy Browkin
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL–02–097 Warsaw, Poland
Email: bro@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01296-5
PII: S 0025-5718(00)01296-5
Keywords: $p$-adic continued fractions, periodicity
Received by editor(s): August 25, 1999
Published electronically: October 18, 2000
Article copyright: © Copyright 2000 American Mathematical Society