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SUMMARY:Joint distribution of primes in multiple short intervals
DTSTART:20260316T100000Z
DTEND:20260316T110000Z
DTSTAMP:20260306T210600Z
UID:indico-event-14763@indico.math.cnrs.fr
CONTACT:regis.de-la-breteche@imj-prg.fr
DESCRIPTION:Speakers: Sun Kai Leung (University of Oxford\, Royaume-Uni)\n
 \nThe study of primes in short intervals goes back to Gauss. Assuming the 
 prime $k$-tuple conjecture\, Montgomery and Soundararajan showed that the 
 number of primes in a short moving interval is asymptotically normal. This
  raises a natural question: What is the joint distribution of weighted pri
 me counts in two or more short intervals?\nAssuming the Riemann hypothesis
  and the linear independence conjecture\, we show that these weighted coun
 ts follow a multivariate Gaussian distribution with weak negative correlat
 ions. I will also discuss several consequences\, viewed as short-interval 
 analogues of results in the Shanks–Rényi prime number race.\n\nhttps://
 indico.math.cnrs.fr/event/14763/
LOCATION:Salle Yvette Cauchois (IHP - Bâtiment Perrin)
URL:https://indico.math.cnrs.fr/event/14763/
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