# How to count (using $\zeta$ functions)

Steffen Højris Pedersen
(Institut for Matematik)
Foredrag for studerende
Fredag, 25 september, 2015, at 15:15-16:00, in Aud. D4 (1531-219)
Abstrakt:

There is a delicate relation between counting the number of primes less then a given $x$, and the Riemann $\zeta$ function

$\zeta(s) = \sum_{n=1}^{\infty} \dfrac{1}{n^s}.$

In the talk I will explain how these two things interact with each other. Furthermore I will explain how the framework of $\zeta$ functions can be used in other counting problems of a similar type.

The talk is going to use results from Complex Analysis, but used as black boxes.