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SUMMARY:Lulu Fang (Nanjing University of Science and Technology)
DTSTART:20211005T123000Z
DTEND:20211005T130000Z
DTSTAMP:20260423T021338Z
UID:OWNS/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/58/">On
  upper and lower fast Khintchine spectra in continued fractions</a>\nby Lu
 lu Fang (Nanjing University of Science and Technology) as part of One Worl
 d Numeration seminar\n\n\nAbstract\nLet $\\psi:\\mathbb{N}\\to \\mathbb{R}
 ^+$ be a function satisfying $\\psi(n)/n\\to \\infty$ as $n \\to \\infty$.
  \nWe investigate from a multifractal analysis point of view the growth sp
 eed of the sums $\\sum^n_{k=1}\\log a_k(x)$ \nwith respect to $\\psi(n)$\,
  where $x=[a_1(x)\,a_2(x)\,\\cdots]$ denotes the continued fraction expans
 ion of $x\\in (0\,1)$. \nThe (upper\, lower) fast Khintchine spectrum is d
 efined as the Hausdorff dimension of the set of points $x\\in(0\,1)$ \nfor
  which the (upper\, lower) limit of $\\frac{1}{\\psi(n)}\\sum^n_{k=1}\\log
  a_k(x)$ is equal to $1$. These three spectra \nhave been studied by Fan\,
  Liao \,Wang \\& Wu (2013\, 2016)\, Liao \\& Rams (2016). In this talk\, w
 e will give a new look \nat the fast Khintchine spectrum\, and provide a f
 ull description of upper and lower fast Khintchine spectra. The latter \ni
 mproves a result of Liao and Rams (2016).\n
LOCATION:https://researchseminars.org/talk/OWNS/58/
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