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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Connections between Galois theory and values of zeta functions

Presented by Leila Schneps, Université de Paris 6

26 October 2009 16:15 in CM 107

There are many ways of generalizing Riemann's zeta functions. One of the simplest to define is the multivariable function zeta(s_1,...,s_r)=sum_{n_1>...>n_r>0} (1/n_1^{s_1}...n_r^{s_r}). This converges if s_1>1. The values zeta(k_1,...,k_r) of these functions at positive integers thus exist if k_1 is at least 2. They are real numbers which form an algebra over Q. Recent results have provided strong evidence for some long-standing conjectures on a very close relation between this algebra and an algebra obtained from the absolute Galois group of Q by considering its action on the thrice-punctured sphere.

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