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SUMMARY:Almost sure convergence of least common multiple of ideals for pol
 ynomials over a number fields
DTSTART:20240312T141500
DTEND:20240312T160000
DTSTAMP:20261001T230456Z
UID:60602a6c0d5bcc46a9e2a547db5a0a1360f65b3a1a8b3acde663e8f7
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ilaria Viglino (EPFL)\nFor f an irreducible polynomial with in
 teger coefficients of degree n\, Cilleruelo's conjecture states that log(l
 cm(f(1)\,...\,f (M))) is asymptotic to (n - 1)M log M\, as M tends to infi
 nity. The Prime Number Theorem for arithmetic progressions can be exploite
 d to obtain an asymptotic estimate when f is a linear polynomial. Cillerue
 lo extended this result to quadratic polynomials. The asymptotic remains u
 nknown for irreducible polynomials of higher degree. Recently the conjectu
 re was shown on average for a large family of polynomials of any degree by
  Rudnick and Zehavi. We investigate the case of S_n-polynomials with coeff
 icients in the ring of algebraic integers of a fixed number field extensio
 n K/Q by considering the least common multiple of ideals in the ring of al
 gebraic integers.
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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