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SUMMARY:Sacha Mangerel (Durham)
DTSTART:20220615T150000Z
DTEND:20220615T160000Z
DTSTAMP:20260418T063835Z
UID:LNTS/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/73/">Ga
 ussian distribution of squarefree and B-free numbers in short intervals</a
 >\nby Sacha Mangerel (Durham) as part of London number theory seminar\n\nL
 ecture held in Room K0.18 in the King's Building.\n\nAbstract\n(Joint with
  O. Gorodetsky and B. Rodgers) It is of classical interest in analytic num
 ber theory to understand the fine-scale distribution of arithmetic sequenc
 es such as the primes. For a given length scale h\, the number of elements
  of a ``nice'' sequence in a uniformly randomly selected interval $(x\,x+h
 ]\, 1 \\leq x \\leq X$\, might be expected to follow the statistics of a n
 ormally distributed random variable (in suitable ranges of $1 \\leq h \\le
 q X$).  Following the work of Montgomery and Soundararajan\, this is known
  to be true for the primes\, but only if we assume several deep and long-s
 tanding conjectures among which the Riemann Hypothesis. \n\nAs a model for
  the primes\, in this talk I will address such statistical questions for t
 he sequence of squarefree numbers\, i.e.\, numbers not divisible by the sq
 uare of any prime\, among other related ``sifted'' sequences called B-free
  numbers. I hope to further motivate and explain our main result that show
 s\, unconditionally\, that short interval counts of squarefree numbers do 
 satisfy Gaussian statistics\, answering several questions of R.R. Hall.\n
LOCATION:https://researchseminars.org/talk/LNTS/73/
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