Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
With V. Golyshev.
This talk is an example of how some cases of Langlands' correspondence for function fields can be interpreted very classically and explicitly. Whenever we have an explicit description of Hecke operators in the Langlands setup, we obtain some elementary identities between special functions. In particular, we see how formulas of Clausen's type and multiplication identities for Bessel functions arise this way.
As an application to arithmetic, our method gives a direct correspondence between solutions of the Dwork's accessory parameter problem as studied by Beukers, and automorphic forms over P^1 with four marked points as described by Kontsevich.