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

Utkarsh Agrawal

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arXiv · 2110.05659

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

Utkarsh Agrawal

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Abstract

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

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Utkarsh Agrawal. 2021-10-12. Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms. https://arxiv.org/abs/2110.05659

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