Erdos-Kac Theorem for the number of prime ideals


Event details

Date 11.10.2023
Hour 16:0017:15
Speaker Mike Cranston (University of Ervine) 

Category Conferences - Seminars
Event Language English

Motivated by the Erdos-Kac Central Limit Theorem, which says that the number of primes dividing a randomly selected number from 1 to N is asymptotically normal as N goes to infinity, we use another method to sample the randomly selected integer The alternative is to select an integer n with probability proportional 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 number of irreducible factors of a randomly (using  a zeta function) selected polynomials with coefficients in a finite field, the number of prime divisors of a randomly selected Gaussian integer, or the number of prime ideals in the factorization of a randomly selected ideal in a Dedekind domain. The talk will be based on joint works with T. Mountford, A. Peltzer and E. Hsu.

Note: 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.

Practical information

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Probability and Stochastic Analysis Seminar