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SUMMARY:Brad Rodgers (Queens University)
DTSTART:20210602T150000Z
DTEND:20210602T160000Z
DTSTAMP:20260423T024745Z
UID:hnts/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/34/">Th
 e distribution of random polynomials with multiplicative coefficients</a>\
 nby Brad Rodgers (Queens University) as part of Heilbronn number theory se
 minar\n\n\nAbstract\nA classic paper of Salem and Zygmund investigates the
  distribution of trigonometric polynomials whose coefficients are chosen r
 andomly (say $+1$ or $-1$ with equal probability) and independently. Salem
  and Zygmund characterized the typical distribution of such polynomials (g
 aussian) and the typical magnitude of their sup-norms (a degree $N$ polyno
 mial typically has sup-norm of size $\\sqrt{N \\log N}$ for large $N$). In
  this talk we will explore what happens when a weak dependence is introduc
 ed between coefficients of the polynomials\; namely we consider polynomial
 s with coefficients given by random multiplicative functions. We consider 
 analogues of Salem and Zygmund's results\, exploring similarities and some
  differences.\n\nSpecial attention will be given to a beautiful point-coun
 ting argument introduced by Vaughan and Wooley which ends up being useful.
 \n\nThis is joint work with Jacques Benatar and Alon Nishry.\n
LOCATION:https://researchseminars.org/talk/hnts/34/
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