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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220610T113622Z
DTSTART:20220614T140000Z
DTEND:20220614T150000Z
SUMMARY:Oleksiy Klurman (University of Bristol) - On the random Chowla c
onjecture
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}q146-kz1e8t
fa-qi8v0m
DESCRIPTION:Abstract : A celebrated conjecture of Chowla in analytic numb
er theory asserts that for the Liouville function $\\lambda(n)$ and any
non-square polynomial $P(n)$ one expects cancellations $\\sum_{n\\le x
}\\lambda(n)=o(x)$ In the case $P(n)=n$ this corresponds to the prime n
umber theorem\, but the conjecture is widely open for any polynomial $P$
of $\\deg P \\ge 2.$ In 1944\, Wintner proposed to study random model
for this question where $\\lambda(n)$ is replaced by a random multiplic
ative function The goal of the talk is to discuss recent advances in un
derstanding the distribution and the size of the largest fluctuations of
appropriately normalized partial sums $\\sum_{n\\le x}f(n)$ (mostly du
e to Harper) and my recent joint work with I. Shkredov and M. Xu aiming
to understand $\\sum_{n\\le x}f(P(n))$ for any polynomial of $\\deg P\\g
e 2.$
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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