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SUMMARY:Trevor D. Wooley (Purdue University)
DTSTART:20250521T153000Z
DTEND:20250521T155500Z
DTSTAMP:20260423T041655Z
UID:CANT2025/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/30/
 ">Equidistribution and $L^p$-sets for $p<2$</a>\nby Trevor D. Wooley (Purd
 ue University) as part of Combinatorial and additive number theory (CANT 2
 025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor).
 \n\nAbstract\nWe investigate subsets $\\mathcal A$ of the natural numbers 
 having the property that\, for some positive number $p<2$\, one has\n\\[\n
 \\int_0^1 \\Bigl| \\sum_{n\\in \\mathcal A\\cap [1\,N]}e(n\\alpha)\\Bigr|^
 p\\\,{\\rm d}\\alpha \\ll |\\mathcal A\\cap [1\,N]|^pN^{\\varepsilon-1}.\n
 \\]\nExamples of such sets include (but are not restricted to) the squaref
 ree\, or more generally\, the $r$-free numbers. For polynomials \n$\\psi(x
 \;\\boldsymbol\\alpha)=\\alpha _kx^k+\\ldots +\\alpha_1x$\, having coeffic
 ients $\\alpha_i$ satisfying suitable irrationality conditions\, we show t
 hat the sequence $(\\psi(n\;\\boldsymbol\\alpha))_{n\\in \\mathcal A}$ is 
 equidistributed modulo $1$.\n
LOCATION:https://researchseminars.org/talk/CANT2025/30/
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