AN ANALOGUE OF MAHLER’S TRANSFERENCE THEOREM FOR MULTIPLICATIVE DIOPHANTINE APPROXIMATION

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详细

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.

作者简介

O. German

Moscow Lomonosov State University; Moscow Center of Fundamental and Applied Mathematics

编辑信件的主要联系方式.
Email: german.oleg@gmail.com
Russian Federation, Moscow; Russian Federation, Moscow

参考

  1. Dyson F.J. On simultaneous Diophantine approximations // Proc. London Math. Soc. 1947. V. 49. № 2. P. 409–420.
  2. German O.N. Transference inequalities for multiplicative Diophantine exponents // Труды МИРАН. 2011. Т. 275. С. 227–239.
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  5. German O.N. On Diophantine exponents and Khintchine’s transference principle // Moscow J. Comb. Number Theory. 2012. V. 2. № 2. P. 22–51.
  6. Герман О.Н., Евдокимов К.Г. Усиление теоремы переноса Малера // Изв. РАН. Сер. матем. 2015. Т. 79. № 1. С. 63–76.
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  9. Mahler K. On compound convex bodies. II. Proc. London Math. Soc. 1955. V. 5. № 3. P. 380–384.

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