On some properties of the constant of the best joint diophantine approximations
https://doi.org/10.22405/2226-8383-2021-22-5-340-345
Abstract
The article considers the question of the behavior of the values of 𝐶𝑛 with increasing 𝑛, where 𝐶𝑛 is the constant of the best joint diophantine approximations. Shows the differences in this question for 𝑙2 and 𝑚𝑎𝑥 norms are shown.
About the Authors
Yurij Aleksandrovich Basalov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
Anastasia Nikolaevna Basalova
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
References
1. Basalov Yu. A. 2019, “Estimations of the constant of the best simultaneous Diophanite approximations“, Chebyshevskii sbornik, Vol. 20, Issue 3, pp. 405–429. https://doi.org/
2. 22405/2226-8383-2019-20-3-405-429
3. Cassels J. W. S. 1955, “Simultaneous Diophantine approximation“, J. London Math. Soc., Vol. 30, pp. 119-121.
4. Cusick T. W. 1980, “Estimates for Diophantine approximation constants“, Journal of Number Theory, Vol. 12 (4), pp. 543–556.
5. Davenport. H., Mahler. K. 1946 “Simultaneous Diophantine approximation“, Duke Math. J., Vol. 1, pp. 105–111.
6. Davenport. H. 1955, “On a theorem of Furtw¨angler“, J. London Math. Soc. , Vol. 30, pp. 186-195.
7. Dirichlet L. G. P. 1842, “Verallgemeinerung eines Satzes aus der Lehre von den Kettenbruchen nebst einigen Anwendungen auf die Theorie der Zahlen“, S. B. Preuss. Akad. Wiss., pp. 93–95.
8. Hurwitz A. 1891, “ ¨Uber die angenaherte Darstellung der Irrationalzahlen durch rationale Briiche“, Math. Ann., Vol. 39, pp. 279-284.
9. Krass S. 1985, “The 𝑁-dimensional diophantine approximation constants“, Australian Mathematical Society , Vol. 32, Is. 2, pp. 313-316.
10. Mack J. M. 1977, “Simultaneous Diophantine approximation“, J. Austral. Math. Soc. A., Vol. 24, pp. 266-285.
11. Nowak W. G. 1981, “A note on simultaneous Diophantine approximation“, Manuscr. Math., Vol. 36, pp. 33-46.
12. Nowak W. G. 2016, “Simultaneous Diophantine approximation: Searching for analogues of Hurwitz’s theorem“, In: T.M. Rassias and P.M. Pardalos (eds.), Essays in mathematics and its applications, Springer, Switzerland, pp. 181-197.
13. Odlyzko A. M. 1990, “Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results“, Journal de Th´eorie des
14. Nombres de Bordeaux, Tome 2, No. 1, pp. 119–141.
15. Spohn W. G. 1968, “Blichfeldt’s theorem and simultaneous Diophantine approximation“, Amer. J. Math., Vol. 90, pp. 885–894.
Review
For citations:
Basalov Yu.A., Basalova A.N. On some properties of the constant of the best joint diophantine approximations. Chebyshevskii Sbornik. 2021;22(5):340-345. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-5-340-345
Views:
308
Email this article 