Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms

Utkarsh Agrawal

paper

Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms

arXiv:2110.05659

Abstract

In this paper we give a formula for the central value of the completed $L$ -function $L (s, S y m^{2} g \times f)$ , where $f$ and $g$ are Hilbert newforms, by explicitly computing the local integrals appearing in the refined Gan-Gross-Prasad conjecture for $S L_{2} \times S L_{2} ~$ . We also work out the rationality of this value in some special cases and give a conjecture for the general case.