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Mathematics of Computation

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Multidimensional $ p$-adic continued fraction algorithms

Authors: Asaki Saito, Jun-ichi Tamura and Shin-ichi Yasutomi
Journal: Math. Comp. 89 (2020), 351-372
MSC (2010): Primary 11J70; Secondary 11J61
Published electronically: June 27, 2019
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Abstract: We give a new class of multidimensional $ p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that the multidimensional $ p$-adic version of Lagrange's Theorem will hold.

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Additional Information

Asaki Saito
Affiliation: Future University Hakodate, Hakodate, Hokkaido 041-8655, Japan

Jun-ichi Tamura
Affiliation: Tsuda College, Kodaira, Tokyo 187-8577, Japan

Shin-ichi Yasutomi
Affiliation: Toho University, Funabashi, Chiba 274-8510, Japan

Keywords: Continued fractions, multidimensional $p$-adic continued fraction algorithms
Received by editor(s): August 7, 2018
Received by editor(s) in revised form: March 26, 2019
Published electronically: June 27, 2019
Additional Notes: This research was supported by JSPS KAKENHI Grant Number 15K00342.
Article copyright: © Copyright 2019 American Mathematical Society