Email this article 
AN ANALOGUE OF MAHLER’S TRANSFERENCE THEOREM FOR MULTIPLICATIVE DIOPHANTINE APPROXIMATION
- Authors: German O.N.1,2
-
Affiliations:
- Moscow Lomonosov State University
- Moscow Center of Fundamental and Applied Mathematics
- Issue: Vol 510, No 1 (2023)
- Pages: 18-22
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2686-9543/article/view/134355
- DOI: https://doi.org/10.31857/S2686954323600015
- EDN: https://elibrary.ru/XHRKPY
- ID: 134355
Cite item
Open Access
Access granted
Subscription Access
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.
About the authors
O. N. German
Moscow Lomonosov State University; Moscow Center of Fundamental and Applied Mathematics
Author for correspondence.
Email: german.oleg@gmail.com
Russian Federation, Moscow; Russian Federation, Moscow
References
- Dyson F.J. On simultaneous Diophantine approximations // Proc. London Math. Soc. 1947. V. 49. № 2. P. 409–420.
- German O.N. Transference inequalities for multiplicative Diophantine exponents // Труды МИРАН. 2011. Т. 275. С. 227–239.
- Касселс Дж.В.С. Введение в теорию диофантовых приближений. М.: ИИЛ, 1961.
- 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.
Supplementary files
