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SUMMARY:Johannes Schleischitz (Middle East Technical University)
DTSTART:20220331T161500Z
DTEND:20220331T173000Z
DTSTAMP:20260423T022036Z
UID:NEDNT/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/45/">E
 xact uniform approximation and Dirichlet spectrum</a>\nby Johannes Schleis
 chitz (Middle East Technical University) as part of New England Dynamics a
 nd Number Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe consid
 er the Dirichlet spectrum\, with respect to maximum norm and simultaneous 
 approximation. It is basically the analogue of the famous (multi-dimension
 al) Lagrange spectrum with respect to uniform approximation. By Dirichlet
 ’s Theorem it is contained in [0\,1]. The central new result is that it 
 equals the entire interval [0\,1] when the number of variables is two or m
 ore. We thereby get a new\, constructive proof of a recent result by Beres
 nevich\, Guan\, Marnat\, Ramirez and Velani that there are Dirichlet impro
 vable vectors that are neither bad nor singular\, in any dimension. We pro
 vide several generalizations\, including metrical claims.\n
LOCATION:https://researchseminars.org/talk/NEDNT/45/
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