Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Wadim Zudilin
Affiliation:

U of Newcastle/MPIM
Date:

Wed, 2016-05-25 14:15 - 15:15 It is a classical fact that the irrationality of a number $\xi\in\mathbb{R}$ follows from

the existence of a sequence $p_n/q_n$ with integral $p_n$ and $q_n$ such that

$q_n\xi-p_n\ne0$ for all $n$ and $q_n\xi-p_n\to0$ as $n\to\infty$. In my talk I

give an extension of this criterion in the case when the sequence possesses an

additional `period' structure; in particular, the requirement $q_n\xi-p_n\to 0$ is

weakened. Some applications are discussed including a new proof of the

irrationality of $\pi$.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246