Linear forms of a given Diophantine type

Oleg N. German[1]; Nikolay G. Moshchevitin[1]

  • [1] Moscow State University Vorobiovy Gory, GSP–2 119992 Moscow, RUSSIA

Journal de Théorie des Nombres de Bordeaux (2010)

  • Volume: 22, Issue: 2, page 383-396
  • ISSN: 1246-7405

Abstract

top
We prove a result on the existence of linear forms of a given Diophantine type.

How to cite

top

German, Oleg N., and Moshchevitin, Nikolay G.. "Linear forms of a given Diophantine type." Journal de Théorie des Nombres de Bordeaux 22.2 (2010): 383-396. <http://eudml.org/doc/116410>.

@article{German2010,
abstract = {We prove a result on the existence of linear forms of a given Diophantine type.},
affiliation = {Moscow State University Vorobiovy Gory, GSP–2 119992 Moscow, RUSSIA; Moscow State University Vorobiovy Gory, GSP–2 119992 Moscow, RUSSIA},
author = {German, Oleg N., Moshchevitin, Nikolay G.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {linear forms; best approximation},
language = {eng},
number = {2},
pages = {383-396},
publisher = {Université Bordeaux 1},
title = {Linear forms of a given Diophantine type},
url = {http://eudml.org/doc/116410},
volume = {22},
year = {2010},
}

TY - JOUR
AU - German, Oleg N.
AU - Moshchevitin, Nikolay G.
TI - Linear forms of a given Diophantine type
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 2
SP - 383
EP - 396
AB - We prove a result on the existence of linear forms of a given Diophantine type.
LA - eng
KW - linear forms; best approximation
UR - http://eudml.org/doc/116410
ER -

References

top
  1. R. K. Akhunzhanov, N. G. Moshchevitin, Vectors of given Diophantine type. Mathematical Notes 80:3 (2006), 318–328. Zbl1156.11325MR2278876
  2. V. Beresnevich, H. Dickinson, S. L. Velani, Sets of “exact logarithmic” order in the theory of Diophantine approximation. Math. Annalen 321 (2001), 253–273. Zbl1006.11039MR1866488
  3. Y. Bugeaud, Sets of exact approximation order by rational numbers. Math. Ann. 327 (2003), 171–190. Zbl1044.11059MR2006007
  4. Y. Bugeaud, Sets of exact approximation order by rational numbers II. Univ. Disrtib. Theory 3 (2008), 9–20. Zbl1219.11014MR2439605
  5. T. W. Cusick, M. E. Flahive, The Markoff and Lagrange spectra. AMS, Providence, Math. surveys and monographs 30, 1989. Zbl0685.10023MR1010419
  6. O. N. German, Asymptotic directions for best approximations of an n -dimensional linear form. (Russian) Mat. Zametki, 75:1 (2004), 55–70; translation in Math. Notes 75:1-2 (2004), 51–65. Zbl1111.11036MR2053149
  7. M. Hall Jr., On the sum and product of continued fractions. Ann. of Math. (2) 48 (1948), 966–993. Zbl0030.02201MR22568
  8. V. Jarnik, Uber die simultanen diophantischen Approximationen. Math. Zeitschr. 33 (1931), 505–543. Zbl57.1370.01MR1545226
  9. V. Jarnik, Un Théorème d’existence pour Les Approximations Diophantiennes. L’Enseignement mathématique 25 (1969), 171–175. Zbl0177.07201MR248088
  10. N. G. Moshchevitin, On simultaneous Diophantine approximations. Vectors of given Diophantine type. Mathematical Notes 61:5 (1997), 590–599. Zbl0916.11040MR1620125

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.