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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220421T104427Z
DTSTART:20220426T140000Z
DTEND:20220426T150000Z
SUMMARY:Demi Allen (University of Exeter) - An inhomogeneous Khintchine–
Groshev Theorem without monotonicity
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}c14a-kz1eee
cu-uszok0
DESCRIPTION:Abstract : The classical (inhomogeneous) Khintchine–Groshev T
heorem tells us that for a monotonic approximating function ?:N?[0\,?) t
he Lebesgue measure of the set of (inhomogeneously) ?-well-approxim
able points in R^{nm} is zero or full depending on\, respectively\, th
e convergence or diver-gence of a volume series. In the homogeneous cas
e\, it is now known that the monotonicity condition on ? can be removed
whenever nm >1\, and cannot be removed when nm= 1. In this talk I will
discuss recent work with Felipe A. Ramirez (Wesleyan\, US) in which we s
how that the inhomogeneous Khintchine–Groshev Theorem is true without th
e monotonicity assumption on ? whenever nm >2. This result brings the i
nhomogeneous theory almost in line with the completed homogeneous theory
. I will survey previous results towards removing monotonicity from the
homogeneous and inhomogeneous Khintchine–Groshev Theorem before discuss
ing the main ideas behind the proof our recent result.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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