TY - JOUR
T1 - The Hausdorff Dimension of Sets of Points Whose Simultaneous Rational Approximation by Sequences of Integer Vectors Have Errors with Small Product
AU - Rynne, B. P.
PY - 1994/7
Y1 - 1994/7
N2 - Let m, n, be positive integers and let Q be an infinite subset of Zn. For any number t, define the set [formula]. It is shown in this paper that if ? ? [0, n] is the unique number such that the series [formula] is convergent when e{lunate} > 0 but divergent when e{lunate} < 0, then the Hausdorff dimension of the set EQ(m, n; t) is dim EQ(m, n; t) = mn - 1 + (1 + ?)/(1 + t), for all t > ?. © 1994 Academic Press. All rights reserved.
AB - Let m, n, be positive integers and let Q be an infinite subset of Zn. For any number t, define the set [formula]. It is shown in this paper that if ? ? [0, n] is the unique number such that the series [formula] is convergent when e{lunate} > 0 but divergent when e{lunate} < 0, then the Hausdorff dimension of the set EQ(m, n; t) is dim EQ(m, n; t) = mn - 1 + (1 + ?)/(1 + t), for all t > ?. © 1994 Academic Press. All rights reserved.
UR - http://www.scopus.com/inward/record.url?scp=43949161623&partnerID=8YFLogxK
U2 - 10.1006/jnth.1994.1053
DO - 10.1006/jnth.1994.1053
M3 - Article
SN - 0022-314X
VL - 48
SP - 75
EP - 79
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -