# Special values of automorphic L-functions

25.01.2022 13:15 - 14:45

Giancarlo Castellano (U Vienna)

Automorphic L-functions are complex functions of a complex variable associated to abstract objects known as automorphic representations. They are the object of intense study in number theory, motivated by the far-reaching conjecture, in the framework of the Langlands programme, that all L-functions and zeta functions of arithmetic interest can be regarded as automorphic L-functions. In particular, there is great interest in their special values, which in a number of cases can be studied by relating them to certain invariants (known as "periods") of the underlying representations. In my dissertation, I specifically look at Rankin–Selberg L-functions for $$\mathrm{GL}_n \times \mathrm{GL}_m$$, with $$n$$ even and $$m < n$$ odd, over a totally real number field.

The structure of the talk will essentially follow the thread given above. In keeping with the spirit of the seminar, the first section will be aimed to be accessible to non-experts.

Organiser:

#### H. Grobner, A. Minguez-Espallargas, A. Mellit

Location:
Zoom-Meeting ID: 431 655 310, Passcode: 0cnL5d