分野別セミナー

[講演概要]
The Rankin-Selberg L-function associated with two automorphic cusp forms is known to have a pole at s=1 if and
only if the two forms are essentially the same.
This result is central in applications, and has been first proved using the method of integral representation of
L-functions.
However, such integral representations naturally exist only for generic representations, leaving aside
important cases.
This motivated Langlands' approach that goes "beyond endoscopy", replacing the use of integral representations by the one of trace formulas.
I will present such an approach in the case of automorphic forms of GL(2) of different types, underlining the
uniformity of the proof between the different types.
This is based on results of Ganguly and Mawia, and a joint project in progress aiming at going beyond.