Abstract
Khintchine’s and Dyson’s transference theorems can be very easily deduced from Mahler’s transference theorem. In the multiplicative setting an obstacle appears, which does not allow deducing the multiplicative transference theorem immediately from Mahler’s theorem. Some extra considerations are required, for instance, induction by the dimension. In this paper we propose an analogue of Mahler’s theorem which implies the multiplicative transference theorem immediately.
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Funding
This research was supported by the Russian Science Foundation, grant no. 22-21-00079, https://rscf.ru/project/22-21-00079/.
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German, O.N. An Analogue of Mahler’s Transference Theorem for Multiplicative Diophantine Approximation. Dokl. Math. 107, 101–104 (2023). https://doi.org/10.1134/S1064562423700680
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DOI: https://doi.org/10.1134/S1064562423700680