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SUMMARY:On The Membership Problem for Hypergeometric Sequences with Ration
 al Parameters
DTSTART:20230321T094500Z
DTEND:20230321T104500Z
DTSTAMP:20260522T144600Z
UID:indico-event-9566@indico.math.cnrs.fr
DESCRIPTION:Speakers: Klara Nosan (IRIF\, Université Paris-Cité)\n\nWe i
 nvestigate the Membership Problem for hypergeometric sequences: given a hy
 pergeometric sequence ⟨u_n⟩ of rational numbers and a rational value t
 \, decide whether t occurs in the sequence. We show decidability of this p
 roblem under the assumption that in the defining recurrence f(n) u_{n+1} =
  g(n) u_n\, the roots of the polynomials f and g are all rational numbers.
  We further show the problem remains decidable if the splitting fields of 
 the polynomials f and g are distinct or if f and g are monic polynomials t
 hat both split over a quadratic number field. Our proof relies on bounds 
 on the density of primes in arithmetic progressions. We also observe a rel
 ationship between the decidability of the Membership problem (and variants
 ) and the Rohrlich-Lang conjecture in transcendence theory. This talk is 
 based on works done in collaboration with George Kenison\, Amaury Pouly\, 
 Mahsa Shirmohammadi and James Worrell.\n\nhttps://indico.math.cnrs.fr/even
 t/9566/
LOCATION:Salle Fokko du Cloux\, Bât Braconnier (ICJ\, Université Lyon 1)
URL:https://indico.math.cnrs.fr/event/9566/
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