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Seminários do IMPA

Física Matemática

Generalised Riemann Hypothesis
Giuseppe Mussardo

SISSA - Trieste
Segunda-feira, 20 de maio de 2019, 10:30
Auditorio Ricardo Mañé

In August 1859 the young and still little known Bernhard Riemann presented a paper to the Berlin Academic titled

On the number of primes less than a given quantity

In the middle of that paper, Riemann made a guess — remark or conjecture — on the zeros of analytic function which controls the growth of the primes. Mathematics has never been the same since.

The seminar presents the captive story behind this problem and discusses how the original conjecture can be extended to all Dirichlet functions, giving rise to the Generalised Riemann Hypothesis for the non-trivial zeros of all these functions. We show that the solution of the Generalised Riemann Hypothesis can be obtained employing ideas and methods which come from statistical physics, i.e. from the stochastic world of random walks and alike.