Abstract
We study Schneider's version of p-adic continued fractions. We are interested in the finiteness of rational number expansion, the quality of approximation by convergents, the irrationality exponent of a number with a given continued fraction expansion, and the convergence of Schneider's continued fractions in the field of real numbers. The main requirement for all of these problems is a good estimate of growth for the sequences of numerators and denominators of convergents.
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The author was supported by the Croatian Science Foundation under the project no. IP- 2018-01-1313 and the QuantiXLie Center of Excellence, a project co-financed by the Croatian Government and European Union through the European Regional Development Fund – the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004).
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Pejković, . Schneider’s p-adic continued fractions. Acta Math. Hungar. 169, 191–215 (2023). https://doi.org/10.1007/s10474-023-01306-w
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DOI: https://doi.org/10.1007/s10474-023-01306-w