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.