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SUMMARY:Products of two random "primes'' in residue classes [MPIM]
DTSTART:20260923T123000Z
DTEND:20260923T133000Z
DTSTAMP:20260926T014400Z
UID:indico-event-1590@math-events.uni-bonn.de
DESCRIPTION:Speakers: Bill Banks (University of Missouri\, Columbia/MPIM)\
 n\nNumber theory lunch seminar\nErdös\, Odlyzko\, and Sárközy conjectur
 ed that every invertible residue class mod $q$ contains a product of two p
 rimes of size at most $q$. This is open even under GRH. After reviewing ra
 ndom models of the primes (Cram\\'er\, Granville\, and the Banks--Ford--Ta
 o sieve model)\, I will show that the analogue of the EOS conjecture holds
 \, in Granville's random model\, almost surely and with both "primes" belo
 w $q^{3/4+\\epsilon}$\, along with a uniform asymptotic count. The arithme
 tic rests on Kloosterman sums\; the probability requirement is minimal. St
 rikingly\, the corresponding statement fails in the sieve model\, so the c
 hoice of model is decisive.\n \n\nhttps://math-events.uni-bonn.de/event/1
 590/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1590/
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