BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Tariq Osman (Brandeis University)
DTSTART:20221201T171500Z
DTEND:20221201T183000Z
DTSTAMP:20260423T022035Z
UID:NEDNT/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/57/">T
 ail Asymptotics for Generalised Theta Sums with Rational Parameters</a>\nb
 y Tariq Osman (Brandeis University) as part of New England Dynamics and Nu
 mber Theory Seminar\n\nLecture held in Online.\n\nAbstract\nWe define gene
 ralised theta sums as exponential sums of the form S^f_N(x\; \\alpha\, \\b
 eta) := \\sum_{n \\in \\mathbb Z} f(n/N) e((1/2 n^2 + \\beta n)x + \\alpha
  n)\, where e(z) = e^{2 \\pi i z}. If \\alpha and \\beta are fixed real nu
 mbers\, and x is chosen randomly from the unit interval\, we may use homog
 eneous dynamics to show that N^{-1/2} S^f_N$ possesses a limiting distribu
 tion as N goes to infinity\, provided f is sufficiently regular. In joint 
 work with F. Cellarosi\, we prove that for specific rational pairs (\\alph
 a\, \\beta) this limiting distribution is compactly supported and that all
  other rational pairs lead to a limiting distribution with heavy tails. Th
 is complements the existing work of F. Cellarosi and J. Marklof where at l
 east one of \\alpha or \\beta is irrational.\n
LOCATION:https://researchseminars.org/talk/NEDNT/57/
END:VEVENT
END:VCALENDAR