Farey maps, Diophantine approximation and Bruhat-Tits tree

Dong Han Kim, Seonhee Lim, Hitoshi Nakada, Rie Natsui

研究成果: Article査読

2 被引用数 (Scopus)

抄録

Based on Broise-Alamichel and Paulin's work on the Gauss map corresponding to the principal convergents via the symbolic coding of the geodesic flow of the continued fraction algorithm for formal power series with coefficients in a finite field, we continue the study of the Gauss map via Farey maps to contain all the intermediate convergents. We define the geometric Farey map, which is given by time-one map of the geodesic flow. We also define algebraic Farey maps, better suited for arithmetic properties, which produce all the intermediate convergents. Then we obtain the ergodic invariant measures for the Farey maps and the convergent speed.

本文言語English
ページ(範囲)14-32
ページ数19
ジャーナルFinite Fields and their Applications
30
DOI
出版ステータスPublished - 2014 11月

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 代数と数論
  • 工学(全般)
  • 応用数学

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