- PII
- 10.31857/S2686954323600015-1
- DOI
- 10.31857/S2686954323600015
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 510 / Issue number 1
- Pages
- 18-22
- 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.
- Keywords
- мультипликативные диофантовы приближения мультипликативные диофантовы экспоненты принцип переноса теорема Малера
- Date of publication
- 17.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 12
References
- 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.
- 3. Касселс Дж.В.С. Введение в теорию диофантовых приближений. М.: ИИЛ, 1961.
- 4. Шмидт В. Диофантовы приближения. М.: “Мир”, 1983.
- 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.
- 7. Mahler K. Ein Übertragungsprinzip für lineare Ungleichungen // Čas. Pešt. Mat. Fys. 1939. V. 68. P. 85–92.
- 8. Mahler K. On compound convex bodies, I. Proc. London Math. Soc. 1955. V. 5. № 3. P. 358–379.
- 9. Mahler K. On compound convex bodies. II. Proc. London Math. Soc. 1955. V. 5. № 3. P. 380–384.
