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Lethbridge Number Theory and Combinatorics Seminar
Date: October 16, 2017
Time: 12 to 12:50 p.m.
Location: C630
Lecturer(s): Lee Troupe (UBC)
Normally Distributed Arithmetic Functions
In the late 1930s, Paul Erdős attended a seminar at Cornell University given by Mark Kac, who suspected that divisibility by primes satisfies a certain "statistical independence" condition. If this were true, the central limit theorem could be used to show that the number of distinct prime factors of n, as n varies over the natural numbers, is normally distributed, with mean loglogn and standard deviation the square root of log log n. Erdős used sieve methods to confirm Kac's intuition, and the resulting Erdős-Kac theorem is a foundational result in the field of probabilistic number theory. Many different proofs of and variations on the Erdős-Kac theorem have been given in the intervening decades. This talk will highlight some of these results and the techniques used to obtain them, including recent work of the speaker and Greg Martin (UBC).
Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science
