Abstract
Our aim in this paper is to study certain sequences of rational approximations in \({\textbf {R}}^2\) and \({\textbf {Q}}_p\) which present some analogy with the continued fractions. We seek to obtain results around the Littlewood conjecture by using approximations of these sorts.
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Acknowledgements
I am extremely grateful to the referee for his careful reading and his useful suggestions. I would also like to thank Yann Bugeaud for his encouragements and our inspiring discussions.
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Communicated by Tim Browning.
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de Mathan, B. On certain simultaneous rational approximations in \({\textbf {R}}^2\) and certain rational approximations in \({\textbf {Q}}_p\). Monatsh Math 200, 849–901 (2023). https://doi.org/10.1007/s00605-022-01773-3
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DOI: https://doi.org/10.1007/s00605-022-01773-3