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SUMMARY:Benjamin Ward (University of York)
DTSTART:20260430T161500Z
DTEND:20260430T173000Z
DTSTAMP:20260513T203848Z
UID:NEDNT/107
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/107/">
 Sets of Exact(er) approximation order</a>\nby Benjamin Ward (University of
  York) as part of New England Dynamics and Number Theory Seminar\n\nLectur
 e held in Online.\n\nAbstract\nI will present joint work with Simon Baker 
 (Loughborough) where we introduce a quantitative notion of exactness withi
 n Diophantine approximation. Given functions Ψ : (0\, ∞) → (0\, ∞) 
 and ω : (0\, ∞) → (0\, 1)\, we study the set of points that are Ψ-we
 ll approximable but not Ψ(1 − ω)-well approximable\, denoted E(Ψ\,ω)
 . This generalises the set of Ψ-exact approximation order as studied by B
 ugeaud (Math. Ann. 2003). We prove results on the cardinality and Hausdorf
 f dimension of E(Ψ\,ω). In particular\, for certain functions Ψ we find
  a critical threshold on ω whereby the set E(Ψ\,ω) drops from positive 
 Hausdorff dimension to empty when ω is multiplied by a constant.\n
LOCATION:https://researchseminars.org/talk/NEDNT/107/
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