Enviar artigo por via de e-mail AN ANALOGUE OF MAHLER’S TRANSFERENCE THEOREM FOR MULTIPLICATIVE DIOPHANTINE APPROXIMATION
- Autores: German O.N.1,2
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Afiliações:
- Moscow Lomonosov State University
- Moscow Center of Fundamental and Applied Mathematics
- Edição: Volume 510 (2023)
- Páginas: 18-22
- Seção: MATHEMATICS
- URL: https://rjeid.com/2686-9543/article/view/647856
- DOI: https://doi.org/10.31857/S2686954323600015
- EDN: https://elibrary.ru/XHRKPY
- ID: 647856
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Resumo
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.
Sobre autores
O. German
Moscow Lomonosov State University; Moscow Center of Fundamental and Applied Mathematics
Autor responsável pela correspondência
Email: german.oleg@gmail.com
Russian Federation, Moscow; Russian Federation, Moscow
Bibliografia
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- Шмидт В. Диофантовы приближения. М.: “Мир”, 1983.
- German O.N. On Diophantine exponents and Khintchine’s transference principle // Moscow J. Comb. Number Theory. 2012. V. 2. № 2. P. 22–51.
- Герман О.Н., Евдокимов К.Г. Усиление теоремы переноса Малера // Изв. РАН. Сер. матем. 2015. Т. 79. № 1. С. 63–76.
- Mahler K. Ein Übertragungsprinzip für lineare Ungleichungen // Čas. Pešt. Mat. Fys. 1939. V. 68. P. 85–92.
- Mahler K. On compound convex bodies, I. Proc. London Math. Soc. 1955. V. 5. № 3. P. 358–379.
- Mahler K. On compound convex bodies. II. Proc. London Math. Soc. 1955. V. 5. № 3. P. 380–384.
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