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- W1859762011 abstract "We consider the diophantine approximation problem <disp-formula content-type=math/mathml> [ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartAbsoluteValue x minus StartFraction p Over q EndFraction EndAbsoluteValue less-than-or-equal-to StartFraction f left-parenthesis log q right-parenthesis Over q squared EndFraction> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>x</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mfrac> <mml:mi>p</mml:mi> <mml:mi>q</mml:mi> </mml:mfrac> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>log</mml:mi> <mml:mo><!-- --></mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfrac> </mml:mrow> <mml:annotation encoding=application/x-tex>left vert x-frac {p}{q}right vert leq frac {f(log q)}{q^2}</mml:annotation> </mml:semantics> </mml:math> ] </disp-formula> where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a fixed function satisfying suitable assumptions. Suppose that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=x> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding=application/x-tex>x</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is randomly chosen in the unit interval. In a series of papers that appeared in earlier issues of this journal, LeVeque raised the question of whether or not the central limit theorem holds for the solution set of the above inequality (compare also with some work of Erdős). Here, we are going to extend and solve LeVeque’s problem." @default.
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- W1859762011 date "2002-12-18" @default.
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- W1859762011 title "On a problem of W. J. LeVeque concerning metric diophantine approximation" @default.
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- W1859762011 doi "https://doi.org/10.1090/s0002-9947-02-03225-7" @default.
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