On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms

Shih-Yu Chen

On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms

Number Theory 2023-01-04 v2

Authors: Shih-Yu Chen

Abstract

We prove an automorphic analogue of Deligne's conjecture for symmetric fourth $L$ -functions of Hilbert modular forms. We extend the result of Morimoto based on generalization and refinement of the results of Grobner and Lin to cohomological irreducible essentially conjugate self-dual cuspidal automorphic representations of ${\rm GL}_2$ and ${\rm GL}_3$ over CM-fields.

Keywords

deligne conjecture symmetric fourth l-functions hilbert modular forms automorphic representations cm-fields cohomology

Cite

@article{arxiv.2101.07507,
  title  = {On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms},
  author = {Shih-Yu Chen},
  journal= {arXiv preprint arXiv:2101.07507},
  year   = {2023}
}

Comments

to be published in Advances in Mathematics. arXiv admin note: text overlap with arXiv:2012.00625

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