An Automorphic translation of Deligne’s conjecture: Special values of L-function attached to an automorphic representation of GL_N over a number field

Zoom Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

I will talk about an arithmetic property of L-functions namely relations of rationality for special values of L-functions attached to a representation. A classical example is “the value of Riemann Zeta function at all positive even integers is equal to an integral power of π up to a rational number”. To see an adelic example, I will discuss algebraicity results for all the critical values of certain Rankin-Selberg L-functions attached to an automorphic representation and a character, for GL(3) × GL(1) over a number field. These algebraicity results are derived from the theory of L-functions by giving a cohomological interpretation to an integral representing a critical L-value in terms of the Poincare pairing. This is joint work with A. Raghuram.