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SUMMARY:Lukas Spiegelhofer (Montanuniversität Leoben)
DTSTART:20201215T133000Z
DTEND:20201215T143000Z
DTSTAMP:20260423T040003Z
UID:OWNS/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/27/">Th
 e digits of $n+t$</a>\nby Lukas Spiegelhofer (Montanuniversität Leoben) a
 s part of One World Numeration seminar\n\n\nAbstract\nWe study the binary 
 sum-of-digits function $s_2$ under addition of a constant $t$.\nFor each i
 nteger $k$\, we are interested in the asymptotic density $\\delta(k\,t)$ o
 f integers $t$ such that $s_2(n+t)-s_2(n)=k$.\nIn this talk\, we consider 
 the following two questions. \n\n(1) Do we have  \\[  c_t=\\delta(0\,t)+\\
 delta(1\,t)+\\cdots>1/2?  \\]\nThis is a conjecture due to T. W. Cusick (2
 011). \n\n(2) What does the probability distribution defined by $k\\mapsto
  \\delta(k\,t)$ look like?\n\nWe prove that indeed $c_t>1/2$ if the binary
  expansion of $t$ contains at least $M$ blocks of contiguous ones\, where 
 $M$ is effective.\nOur second theorem states that $\\delta(j\,t)$ usually 
 behaves like a normal distribution\, which extends a result by Emme and Hu
 bert (2018).\n\nThis is joint work with Michael Wallner (TU Wien).\n
LOCATION:https://researchseminars.org/talk/OWNS/27/
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