Demi Allen (University of Exeter) - An inhomogeneous Khintchine–Groshev Theorem without monotonicity
| Dates: | 26 April 2022 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |
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| Speaker: | Demi Allen |
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Abstract : The classical (inhomogeneous) Khintchine–Groshev Theorem tells us that for a monotonic approximating function ?:N?[0,?) the Lebesgue measure of the set of (inhomogeneously) ?-well-approximable points in R^{nm} is zero or full depending on, respectively, the convergence or diver-gence of a volume series. In the homogeneous case, 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 show that the inhomogeneous Khintchine–Groshev Theorem is true without the monotonicity assumption on ? whenever nm >2. This result brings the inhomogeneous 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 discussing the main ideas behind the proof our recent result.
Speaker
Demi Allen
Organisation: University of Exeter
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
