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

Utkarsh Agrawal

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

Number Theory 2025-01-14 v4

Authors: Utkarsh Agrawal

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.

Keywords

degree six l-function central value hilbert modular form gan-gross-prasad conjecture local integral rationality

Cite

@article{arxiv.2110.05659,
  title  = {Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms},
  author = {Utkarsh Agrawal},
  journal= {arXiv preprint arXiv:2110.05659},
  year   = {2025}
}

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