Speaker: Lin Weng, Kyushu University </br>
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Title: Non-Abelian L Functions </br>
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Abstract: </br>
We begin our talk with a matrix version of Artin L functions.
Then to motivate our construction of non-abelain L functions,
we explain the non-abelain class field theory for Riemann surfaces
using stable parabolic bundles. After that, we introduce our
new yet genuine non-abelian zeta functions for number fields.
Standard properties such as meromorphic continuation,
functional equation and singularities will be discussed.
In particular, we show that in the case of rank two,
all zeros of such zetas lie on the line of real part a half.
Now based on the fact that our zetas can be understood
as integrations of Epstein zeta functions,
we then use Langlands' fundamental theory on Eisenstein series
to define and study non-abelian L functions, within which
all Artin L are supposed to be natrually included. If time is allowed
we will indicate how such non-abelian L functions are naturally
related with Arthur's periods and how they can be calculated
using an advanced version of Rankin-Selberg method
due to Jacquet-Lapid-Rogawski.