MathematischeGesellschaft Special values of L-functions: old and new |  |
Speaker:Prof. Dr. Günter Harder, Universität Bonn
Organizer:Mathematisches Institut
Details:
At first I will recall some classical results about special values of L-functions
(Euler, Leibniz). Then I will try to explain how these formulas fit into the general
circle of ideas about special values of L− functions, I will explain in a somewhat
vague way the concept of (motivic or automorphic) L− functions and I will provide
some more explicit examples of L-functions.
After that I will formulate the Deligne conjecture about critical values of motivic L-functions.
I will explain certain modifications of these conjectures, which in a sense are
weaker but in some sense also more precise, because it is possible to fix the periods
up to a unit. Finally I discuss the influence of these special values on the structure
of the cohomology of arithmetic groups as module under the Hecke algebra.
(Euler, Leibniz). Then I will try to explain how these formulas fit into the general
circle of ideas about special values of L− functions, I will explain in a somewhat
vague way the concept of (motivic or automorphic) L− functions and I will provide
some more explicit examples of L-functions.
After that I will formulate the Deligne conjecture about critical values of motivic L-functions.
I will explain certain modifications of these conjectures, which in a sense are
weaker but in some sense also more precise, because it is possible to fix the periods
up to a unit. Finally I discuss the influence of these special values on the structure
of the cohomology of arithmetic groups as module under the Hecke algebra.
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Type:Colloquium
Language:English
Category:Research
Host:Prof. V. Blomer
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Direct link to event:https://events.goettingen-campus.de/event?eventId=8519
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