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SUMMARY:Nikos Frantzikinakis (Crete)
DTSTART:20200720T160000Z
DTEND:20200720T170000Z
DTSTAMP:20260423T035752Z
UID:WAC/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WAC/13/">Erg
 odic properties of the Liouville function and applications</a>\nby Nikos F
 rantzikinakis (Crete) as part of Webinar in Additive Combinatorics\n\n\nAb
 stract\nThe Liouville function is a multiplicative function that encodes i
 mportant information related to distributional properties of the prime num
 bers. A conjecture of Chowla states that the values of the Liouville funct
 ion fluctuate between plus and minus in such a random way\, that all sign 
 patterns of a given length appear with the same frequency. The Chowla conj
 ecture remains largely open and in this talk we will see how ergodic theor
 y combined with some feedback from number theory allows us to establish tw
 o variants of this conjecture. Key to our approach is an in-depth study of
  measure preserving systems that are naturally associated with the Liouvil
 le function. The talk is based on joint work with Bernard Host.\n
LOCATION:https://researchseminars.org/talk/WAC/13/
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