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

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Speaker: 
Gunja Sachdeva
Affiliation: 
Indian Institute of Science Education and Research/MPIM
Date: 
Wed, 2021-01-27 14:30 - 15:30
Parent event: 
Number theory lunch seminar

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.

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