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A determinantal approach to irrationality

Posted in
Speaker: 
Wadim Zudilin
Affiliation: 
U of Newcastle/MPIM
Date: 
Wed, 2016-05-25 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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 $\pi$.

 

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