Archivio Istituzionale della RicercaContinued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of p-adic continued fractions, i.e., continued fractions defined over the field of p-adic numbers Qp, which in the last years has recorded a considerable increase of interest and research activity. We start from the very first definitions up to the most recent developments and open problems.
Continued fractions in the field of p-adic numbers / Romeo, Giuliano. - In: BULLETIN (NEW SERIES) OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0273-0979. - 61:2(2024), pp. 343-371. [10.1090/bull/1819]
Continued fractions in the field of p-adic numbers
Romeo, Giuliano
2024
Abstract
Continued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of p-adic continued fractions, i.e., continued fractions defined over the field of p-adic numbers Qp, which in the last years has recorded a considerable increase of interest and research activity. We start from the very first definitions up to the most recent developments and open problems.
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https://hdl.handle.net/11583/2991187