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SUMMARY:Demi Allen (University of Warwick)
DTSTART:20211028T161500Z
DTEND:20211028T173000Z
DTSTAMP:20260423T021932Z
UID:NEDNT/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/33/">A
 n inhomogeneous Khintchine-Groshev Theorem without monotonicity</a>\nby De
 mi Allen (University of Warwick) as part of New England Dynamics and Numbe
 r Theory Seminar\n\nLecture held in Online.\n\nAbstract\nThe classical (in
 homogeneous) Khintchine-Groshev Theorem tells us that for a monotonic appr
 oximating function $\\psi: \\mathbb{N} \\to [0\,\\infty)$ the Lebesgue mea
 sure of the set of (inhomogeneously) $\\psi$-well-approximable points in $
 \\mathbb{R}^{nm}$ is zero or full depending on\, respectively\, the conver
 gence or divergence of $\\sum_{q=1}^{\\infty}{q^{n-1}\\psi(q)^m}$. In the 
 homogeneous case\, it is now known that the monotonicity condition on $\\p
 si$ can be removed whenever $nm>1$ and cannot be removed when $nm=1$. In t
 his talk I will discuss recent work with Felipe A. Ramírez (Wesleyan\, US
 ) in which we show that the inhomogeneous Khintchine-Groshev Theorem is tr
 ue without the monotonicity assumption on $\\psi$ whenever $nm>2$. This re
 sult brings the inhomogeneous theory almost in line with the completed hom
 ogeneous theory. I will survey previous results towards removing monotonic
 ity from the homogeneous and inhomogeneous Khintchine-Groshev Theorem befo
 re discussing the main ideas behind the proof our recent result.\n
LOCATION:https://researchseminars.org/talk/NEDNT/33/
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