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SUMMARY:Chris Lutsko (Rutgers University)
DTSTART:20211111T171500Z
DTEND:20211111T183000Z
DTSTAMP:20260423T022034Z
UID:NEDNT/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/35/">P
 air correlation of monomial sequences modulo 1</a>\nby Chris Lutsko (Rutge
 rs University) as part of New England Dynamics and Number Theory Seminar\n
 \nLecture held in Online.\n\nAbstract\nFix $\\alpha\, \\theta > 0$\, and c
 onsider the sequence $(\\alpha n^\\theta \\mod 1)_{n>0}$. Since the semina
 l work of Rudnick-Sarnak (1998)\, and due to the Berry-Tabor conjecture in
  quantum chaos\, the fine-scale properties of these dilated mononomial seq
 uences have been intensively studied. In this talk\, I will briefly survey
  what is known about these sequences and present a recent result (joint wi
 th Sourmelidis and Technau) showing that for $\\theta \\le 1/3$\, and $\\a
 lpha > 0$\, the pair correlation function is Poissonian. While the techniq
 ues we use are derived from analytic number theory\, the problem is rooted
  in dynamics and relates to dynamical proofs for related problems.\n
LOCATION:https://researchseminars.org/talk/NEDNT/35/
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