À¶Ý®ÊÓƵ

Jeremy Champagne, University of À¶Ý®ÊÓƵ 

On the generalisation of a theorem of Watson

This talk is a continuation of the one I gave in March. In essence, we are discussing the set of real valued functions f(n) such that gcd(n,[f(n)])=1 happens with probability 1/zeta(2) (in the sense of natural densities), and related problems. I will give a general gameplan to establishing such results, and I will prove that gcd(n, [alpha_1n], [alpha_2n^2],...,[alpha_kn^k])=1 happens with probability 1/zeta(k+1) foralpha_1,...,alpha_k irrational.

MC 5403