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SUMMARY:Hamed Mousavi (Georgia Tech)
DTSTART:20200603T193000Z
DTEND:20200603T195500Z
DTSTAMP:20260423T011223Z
UID:CANT2020/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/44/
 ">A class of sums with unexpectedly high cancellation</a>\nby Hamed Mousav
 i (Georgia Tech) as part of Combinatorial and additive number theory (CANT
  2021)\n\n\nAbstract\nA class of sums with unexpectedly high cancellation\
 nAbstract: In this talk we report on the discovery of a general principle 
 leading to\nan unexpected cancellation of oscillating sums\, of which $\\s
 um_{n^2\\leq x}(-1)^ne^{\\sqrt{x-n^2}}$\nis an example (to get the idea of
  the result). It turns out that sums in the\nclass we consider are much sm
 aller than would be predicted by certain\nprobabilistic heuristics. After 
 stating the motivation\,\nwe show a number of results in integer partition
 s. For instance we show a ``weak" version of pentagonal number theorem \n$
 $\n\\sum_{\\ell^2 < x} (-1)^\\ell p(x-\\ell^2)\\ \\sim\\ 2^{-3/4} x^{-1/4}
  \\sqrt{p(x)}\,\n$$\nwhere $p(x)$ is the usual partition function. \n\nJoi
 nt work with Ernie Croot.\n
LOCATION:https://researchseminars.org/talk/CANT2020/44/
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