### 17 oktober 2005, kl 13.15-14.15, Uppsala, rum 3:513.

###
Andrew Booker (University of Michigan):
On decidability of Artin's conjecture

**Abstract.**
Let K be a finite Galois extension of the rationals and rho a complex
representation of the Galois group Gal(K/Q). In 1923, Artin attached
to this data an L-function, L(s,rho), which he conjectured has
analytic continuation to the complex plane and satisfies a functional
equation relating s to 1-s. Through the development of class field
theory and a theorem of Brauer (1947), we know today that Artin's
L-functions are meromorphic in the plane. However, despite this and
more recent progress related to the Langlands program, the full
conjecture remains largely unsolved. I will survey what is known
about Artin's conjecture, why it is important, and address the simpler
question of whether specific instances of the conjecture can be
verified in finite time.