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Klara Courteaut: The Riemann zeta function and its connection to the prime numbers

Time: Fri 2019-03-08 15.15 - 16.00

Location: Room 3418, Lindstedtsvägen 25, 4th floor, Department of Mathematics, KTH

Lecturer: Klara Courteaut

The Riemann zeta function is well-known amongst mathematicians and even those outside of mathematics, possibly due to its involvement in one of the millenium prize problems, the Riemann Hypothesis, which states that all its complex zeros lie on the vertical line passing through 1/2. What is maybe less well known is that the distribution of these zeros is connected to the asymptotic distribution of the prime numbers. In this talk I will explain this connection, first by showing that both Euclid's theorem and the prime number theorem follow from facts about the zeta function, and then by giving the implications of the Riemann hypothesis for the prime numbers. If time permits I will also give some connections to random matrix theory.