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SUMMARY:Alon Agin (Tel Aviv University)
DTSTART:20250318T161500Z
DTEND:20250318T173000Z
DTSTAMP:20260423T021931Z
UID:NEDNT/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/86/">T
 he Dirichlet spectrum</a>\nby Alon Agin (Tel Aviv University) as part of N
 ew England Dynamics and Number Theory Seminar\n\nLecture held in Online.\n
 \nAbstract\nAkhunzhanov and Shatskov defined the Dirichlet spectrum\, corr
 esponding to mxn matrices and to norms on R^m and R^n. In case (m\,n) = (2
 \,1) and using the Euclidean norm on R^2\, they showed that the spectrum i
 s an interval. We generalize this result to arbitrary (m\,n) with max(m\,n
 )>1 and arbitrary norms\, improving previous works from recent years. We a
 lso define some related spectra and show that they too are intervals. We a
 lso prove the existence of matrices exhibiting special properties with res
 pect to their uniform exponent. Our argument is a modification of an argum
 ent of Khintchine from 1926.\n
LOCATION:https://researchseminars.org/talk/NEDNT/86/
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