BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:6677@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20200929T111500
DTEND;TZID=Europe/Paris:20200929T121500
DTSTAMP:20241120T201935Z
URL:https://www.i2m.univ-amu.fr/evenements/titre-a-preciser-lukas-spiegelh
 ofer/
SUMMARY:Lukas Spiegelhofer (TU Vienna): The digits of n+t - Lukas Spiegelho
 fer
DESCRIPTION:Lukas Spiegelhofer: We study the binary sum-of-digits function 
 s₂ under addition of a constant t∈ℕ.\nFor each integer j\, we are in
 terested in the asymptotic density\nδ(j\, t) = dens{n∈ℕ : s₂(n+t) -
  s₂(n) = j}.\nIn this talk\, we consider the following two questions.\n(
 1) Do we have\nct = δ(0\, t) + δ(1\, t) + … &gt\; 1/2 ?\nThis is a con
 jecture due to T. W. Cusick (2011).\n(2) What does the probability distrib
 ution defined by j ↦ δ(j\, t) look like?\n\nWe prove that indeed ct &gt
 \; 1/2 if the binary expansion of t contains at least M₀ blocks of conti
 guous 1's\, where M₀ is an absolute\, effective constant.\nNote that the
  number of exceptional t&lt\;T can easily be bounded by some power of log 
 T.\n\nOur second theorem states that δ(j\, t) usually behaves like a norm
 al distribution.\nIf M is the number of blocks of 1's in t\, where M ≥ M
 ₀\, we have\nδ(j\, t) = 1/√(2πv) exp( -j²/(2v) ) + O(M⁻¹(log M)
 ⁴)\,\nuniformly for j∈ℤ and with an absolute implied constant.\nHere
  the variance v depends (explicitly) on the binary expansion of t.\n\nThis
  is joint work with Michael Wallner (TU Wien).
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/09/Lukas-Spiegelhofer.jpg
CATEGORIES:Séminaire,Ernest,Virtual event
LOCATION:Luminy - CIRM\, 163 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy - CIRM:geo:0,0
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:DAYLIGHT
DTSTART:20200329T030000
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
END:DAYLIGHT
END:VTIMEZONE
END:VCALENDAR