On optimal constants for best two-dimensional simultaneous diophantine approximations

Authors
Kratz, W
Citation
W. Kratz, On optimal constants for best two-dimensional simultaneous diophantine approximations, MONATS MATH, 128(2), 1999, pp. 99-110
Citations number
17
Categorie Soggetti
Mathematics
Journal title
MONATSHEFTE FUR MATHEMATIK
ISSN journal
00269255 → ACNP
Volume
128
Issue
2
Year of publication
1999
Pages
99 - 110
Database
ISI
SICI code
0026-9255(1999)128:2<99:OOCFBT>2.0.ZU;2-D
Abstract
The main results of this paper state-optimal constants for estimates of so- called successive minima in two dimensions under a constraint on the denomi nator. While these inequalities are known for every dimension, best possibl e constants within these estimates are, of course, not known for any dimens ion larger than one and remain unknown for all dimensions larger than two.