GENERAL
SEMINAR

“$\phi$ and $\sigma$: from
Euler to Erdos”

by

Florian Luca

(Instituto de Matematicas de la UNAM, MEXICO)

Abstract: In the
first part of this talk, we will survey various old and new results related to
the distribution of the values of the Euler function $\phi(n)$ and the sum of
divisors function $\sigma(n)$ of a positive integer n, their popular values,
their champions, as well as to the distribution of those positive integers
satisfying certain equations involving such functions, like the perfect numbers
and the amicable numbers. In the second part of the talk, we will give some of
the ideas involved in a proof of a recent result obtained jointly with Kevin
Ford and Carl Pomerance which says that there are
infinitely common values in the ranges of these two functions. This settles a
50 year old question of Paul Erdos.

Date : October 17, 2012 (Wednesday)

Time : 15.40-16.30

Place: Bilkent University ,Mathematics Seminar Room SA141

Tea and cookies will be served before the seminar.