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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Correlations of multiplicative functions at almost
all scales - Joni Teräväinen\, University of Oxfo
rd
DTSTART;TZID=Europe/London:20181107T134500
DTEND;TZID=Europe/London:20181107T144500
UID:TALK114055AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/114055
DESCRIPTION:Understanding how shifts of multiplicative functio
ns correlate with each other is a central question
in multiplicative number theory. A well-known con
jecture of Elliott predicts that there should be n
o correlation between shifted multiplicative funct
ions unless the functions involved are ‘pretentiou
s functions’ in a certain precise sense. The Ellio
tt conjecture implies as a special case the famous
Chowla conjecture on shifted products of the Möbi
us function.\n\nIn the last few years\, there has
been a lot of exciting progress on the Chowla and
Elliott conjectures\, and we give an overview of t
his. Nearly all of the previously obtained results
have concerned correlations that are weighted log
arithmically\, and it is an interesting question w
hether one can remove these logarithmic weights. W
e show that one can indeed remove logarithmic aver
aging from the known results on the Chowla and Ell
iott conjectures\, provided that one restricts to
almost all scales in a suitable sense.
LOCATION:MR5\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
CONTACT:Aled Walker
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