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Hausdorff Dimension and Generalized Simultaneous Diophantine Approximation
Author(s) -
Rynne Bryan P.
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398004536
Subject(s) - mathematics , hausdorff dimension , generalization , integer (computer science) , diophantine approximation , diophantine equation , mathematics subject classification , dimension (graph theory) , hausdorff measure , set (abstract data type) , discrete mathematics , hausdorff space , dimension function , infinity , effective dimension , combinatorics , mathematical analysis , computer science , programming language
Suppose that m is a positive integer, τ = ( τ 1 , … , τ m ) ∈ R + mis a vector of strictly positive numbers, and Q is an infinite set of positive integers. Let W Q ( m ; τ) be the set [formula] In this paper we obtain the Hausdorff dimension of this set. We also consider a generalization of the set W Q ( m ; τ), where the error termsq − τ iin the inequalities are replaced by ψ i ( q ), for general functions ψ i satisfying a certain condition at infinity. 1991 Mathematics Subject Classification 11J83, 28A78.