# The popularity of values of Euler’s function

Posted in
Speaker:
Paul Pollack
Affiliation:
University of Georgia
Date:
Wed, 2019-11-13 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

For each positive integer $m$, let $N(m)$ denote the number of $\varphi$-preimages of $m$, where $\varphi$ is Euler’s totient function. For example, $N(12) = 6$, corresponding to the six preimages 13, 21, 26, 28, 36, and 42. We discuss several statistical questions concerning $N(m)$ — for instance, its average size, its maximal order, and the typical size of
$N(\varphi(k))$ as $k$ varies.

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