#### Alladi Ramakrishnan Hall

#### A central value formula of degree 6 complex L-series and arithmetic applications

#### Aprameyo Pal

##### Universitat Duisburg-Essen

*We prove an explicit central value formula for a family of*

complex L-series of degree 6 for GL2 × GL3 which arise as factors of

certain Garret--Rankin triple product L-series associated with modular

forms. Our result generalizes a previous formula of Ichino involving

Saito--Kurokawa lifts, and as an application, we prove Deligne's

conjecture about the algebraicity of the central values of the

considered L-series up to the relevant periods. I would also include

some other arithmetic applications towards the subconvexity problem,

construction of associated p-adic L function, etc.

This is joint work with Carlos de Vera Piquero.

Done