{"id":7236,"date":"2018-10-12T09:47:19","date_gmt":"2018-10-12T07:47:19","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-en\/events\/mini-course-probabilistic-methods-and-value-distribution-of-the-riemann-zeta-function\/"},"modified":"2018-10-12T09:47:19","modified_gmt":"2018-10-12T07:47:19","slug":"mini-course-probabilistic-methods-and-value-distribution-of-the-riemann-zeta-function","status":"publish","type":"events","link":"https:\/\/www.uni.lu\/fstm-en\/events\/mini-course-probabilistic-methods-and-value-distribution-of-the-riemann-zeta-function\/","title":{"rendered":"Mini-course: Probabilistic methods and value distribution of the Riemann zeta function"},"content":{"rendered":"

mini-course by Ashkan Nikeghbali<\/a> from the University of Z\u00fcrich<\/p>

Title: Probabilistic methods and value distribution of the Riemann zeta function<\/p>

Abstract: It is conjectured, since the work of Montgomery, that the zeros of the Riemann zeta function and its values on the critical line have the same behaviour as the eigenvalues of large random (unitary) matrices, as well as some remarkable random variables associated with them (e.g. the characteristic polynomial). In this set of lectures, we shall present the so called “random matrix approach in number theory”. We will start from first principles, by exploring the basic features of some classical matrix ensembles, as well as by establishing some elementary properties of the Riemann zeta function. After this, we shall give a rather detailed presentation of some of the classical random matrix computations underlying the two main conjectures in the field: the Montgomery conjecture and the Keating-Sanith conjecture. We shall adopt a more recent probabilistic point of view on some of these calculations. Our goal will be to show that some of these conjectures are theorems for other arithmetic functions and uncover some possibly universal behaviour.<\/p>

<\/p>

Monday 22 October 2018<\/p>

14:00 – 16:15<\/p>

Room 1.030<\/p>

Tuesday 23 October 2018<\/p>

14:00 – 16:15<\/p>

Room 1.050<\/p>

Wednesday 24 Obtober 2018<\/p>

10:45 – 13:00<\/p>

Room 1.050<\/p>

Monday 29 October 2018<\/p>

14:00 – 16:15<\/p>

Room 1.030<\/p>

Tuesday 30 October 2018<\/p>

10:45 – 13:00<\/p>

Room1.020<\/p><\/div><\/section>","protected":false},"excerpt":{"rendered":"

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