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SUMMARY:Erdos-Kac Theorem for the number of prime ideals
DTSTART;VALUE=DATE-TIME:20231011T160000
DTEND;VALUE=DATE-TIME:20231011T171500
DTSTAMP;VALUE=DATE-TIME:20240414T161816Z
UID:2c910cb3b14f9eb4533820aaad6506e648d57d5c5bd119dcba008866
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mike Cranston (University of Ervine) \n\n \nMotivated by the
Erdos-Kac Central Limit Theorem\, which says that the number of primes d
ividing a randomly selected number from 1 to N is asymptotically normal as
N goes to infinity\, we use another method to sample the randomly select
ed integer The alternative is to select an integer n with probability pro
portional to 1/n^s with proportionality constant 1/\\zeta(s) where \\zeta
(s) is the Riemann zeta function. Techniques were developed in joint work
with T. Mountford to provide a rather easy proof of the above mentioned
Central Limit Theorem. The method works as well when applied to the numbe
r of irreducible factors of a randomly (using a zeta function) selected
polynomials with coefficients in a finite field\, the number of prime di
visors of a randomly selected Gaussian integer\, or the number of prime i
deals in the factorization of a randomly selected ideal in a Dedekind dom
ain. The talk will be based on joint works with T. Mountford\, A. Peltzer
and E. Hsu.\n\nNote: The Probaiblity and Stochastic Analysis semianr is
usually given in two parts\, separated by a break. The first part is about
30 minues explainign the result. The second part is on technical asspects
.
LOCATION:Bernoulli Center https://maps.app.goo.gl/LGa7ei1hQkCkkHN1A
STATUS:CONFIRMED
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