Preview

Doklady of the National Academy of Sciences of Belarus

Advanced search

Generalizing Khinchin’s theorem to a linear combination of analytical linearly independent functions

https://doi.org/10.29235/1561-8323-2019-63-2-135-141

About the Authors

V. I. Bernik
Institute of Mathematics of the National Academy of Sciences of Belarus.
Belarus

Bernik Vasiliy Ivanovich - D. Sc. (Physics and Mathe­matics), Professor, Chief researcher. 

11, Sur- ganov Str., 220072, Minsk.



V. N. Budarina
Dundalk Institute of Technology.
Ireland

Budarina Nataliya Viktorovna - D. Sc. (Physics and Ma­thematics). 

A91 K584, Dublin Road, Dundalk.



H. O’Donnell
Dublin Institute of Technology.
Ireland

O'Donnell Hugh - Ph. D. (Physics and Mathematics).

D02 HW71, Aungier Str., Dublin.



References

1. Khintchine A. Einige Satze uber Kettenbruche, mit Anwendungen auf die Theorie der Diophantischen Approxima- tionen. Mathematische Annalen, 1924, vol. 92, no. 1-2, pp. 115-125 (in German). https://doi.org/10.1007/bf01448437

2. Khintchine A. Uber eine Klasse linear diophantischer Approximationen. Rendiconti del CircoloMatematico di Paler¬mo, 1926, vol. 50, no. 2, pp. 170-195 (in German). https://doi.org/10.1007/bf03014726

3. Mahler K. Uber das MaB der Menge aller S-Zahlen. Mathematische Annalen, 1932, Vol. 106, no. 1, pp. 131-139 (in Ger¬man). https://doi.org/10.1007/bf01455882

4. Kubilius J. On an application of I. M. Vinogradov’s method to the solution of a problem of the metrical theory of num-bers. Doklady Akademii Nauk SSSR, 1949, vol. 67, no. 5, pp. 783-786 (in Russian).

5. Volkmann B. The real cubic case of Mahler’s conjecture. Mathematika, 1961, vol. 8, no. 1, pp. 55-57. https://doi. org/10.1112/s0025579300002126

6. Sprindzuk V. A proof of Mahler’s conjecture on measure of the set of S-numbers. Izvestiya Akademii nauk, seriya ma- tematicheskaya, 1965, vol. 29, pp. 379-436.

7. Sprindzhuk V. G. The problem of Mahler in metric number theory. Minsk, 1967. 184 p. (in Russian).

8. Beresnevich V., Bernik V., Dickinson H., Dodson M. The Khintchine-Groshev Theorem for Planar Curves. Procee¬dings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1999, vol. 455, no. 1988, pp. 3053-3063. https://doi.org/10.1098/rspa.1999.0439

9. Bernik V. I. On the exact order of approximation to zero with values of integral polynomials. Acta Arithmetica, 1989, vol. 53, no. 1, pp. 17-28 (in Russian).

10. Beresnevich V., Bernik V. A Baker’s conjecture and Hausdorff dimension. Publicationes Mathematicae Debrecen, 2000, vol. 54, no. 3-4, pp. 263-269.

11. Beresnevich V., Bernik V., Kleinbock D., Margulis G. Metric Diophantine approximation: The Kleinbock-Groshev theorem for nondegenerate manifolds. Moscow Mathematical Journal, 2002, vol. 2, no. 2, pp. 203-225. https://doi.org/ 10.17323/1609-4514-2002-2-2-203-225

12. Bernik V., Kleinbock D., Margulis G. Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions. International Mathematics Research Notices, 2001, vol. 2001, no. 9, pp. 453-486. https://doi.org/ 10.1155/s1073792801000241

13. Baker A., Schmidt W. Diophantine approximation and Hausdorff dimension. Proceedings of the London Mathematical Society, 1970, vol. s3-21, no 1, pp. 1-11. https://doi.org/10.1112/plms/s3-21.1.1

14. Bernik V. I. Application of the Hausdorff dimension in the theory of Diophantine approximations. Acta Arithmetica, 1983, vol. 42, no. 3, pp. 219-253 (in Russian).

15. Kleinbock D., Backer A. Sprindzuk conjectures for complex analytic manifolds. Algebraic groups. Tata Institute of Fundamental Research, Mambai, 2004, pp. 539-553.


Review

Views: 866


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)