A note on the theorem of Jarník-Besicovitch
1997 ◽
Vol 39
(2)
◽
pp. 233-236
◽
Keyword(s):
This note draws together and extends two recent results on Diophantine approximation and Hausdorff dimension. The first, by Hinokuma and Shiga [12], considers the oscillating error function | sinq|/qτ rather than the strictly decreasing function qτ of Jarnik's theorem. The second is Rynne's extension [17] to systems of linear forms of Borosh and Fraenkel's paper [3] on restricted Diophantine approximation with real numbers. Rynne's result will be extended to a class of general error functions and applied to obtain a more general form of [12] in which the error function is any positive function.
2014 ◽
Vol 91
(1)
◽
pp. 34-40
◽
Keyword(s):
2006 ◽
Vol 48
(02)
◽
pp. 187
◽
2014 ◽
Vol 36
(1)
◽
pp. 1-22
◽
Keyword(s):
2012 ◽
Vol 09
(01)
◽
pp. 77-90
◽
Keyword(s):
Keyword(s):
2016 ◽
Vol 59
(2)
◽
pp. 349-357
◽
Keyword(s):
1966 ◽
Vol 62
(4)
◽
pp. 637-642
◽
Keyword(s):