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SUMMARY:Correlations of multiplicative functions at almost all scales - Jo
 ni Teräväinen\, University of Oxford
DTSTART:20181107T134500Z
DTEND:20181107T144500Z
UID:TALK114055@talks.cam.ac.uk
CONTACT:Aled Walker
DESCRIPTION:Understanding how shifts of multiplicative functions correlate
  with each other is a central question in multiplicative number theory. A 
 well-known conjecture of Elliott predicts that there should be no correlat
 ion between shifted multiplicative functions unless the functions involved
  are ‘pretentious functions’ in a certain precise sense. The Elliott c
 onjecture implies as a special case the famous Chowla conjecture on shifte
 d products of the Möbius function.\n\nIn the last few years\, there has b
 een a lot of exciting progress on the Chowla and Elliott conjectures\, and
  we give an overview of this. Nearly all of the previously obtained result
 s have concerned correlations that are weighted logarithmically\, and it i
 s an interesting question whether one can remove these logarithmic weights
 . We show that one can indeed remove logarithmic averaging from the known 
 results on the Chowla and Elliott conjectures\, provided that one restrict
 s to almost all scales in a suitable sense.
LOCATION:MR5\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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