Continued fractions in local fields, II

Browkin, Jerzy

doi:10.1090/S0025-5718-00-01296-5

Continued fractions in local fields, II
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by Jerzy Browkin PDF

Math. Comp. 70 (2001), 1281-1292 Request permission

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 $p.$

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