Non-abelian base change for symmetric power liftings of holomorphic modular forms

Laurent Clozel; James Newton; Jack A. Thorne

Non-abelian base change for symmetric power liftings of holomorphic modular forms

Number Theory 2024-06-10 v2

Authors: Laurent Clozel , James Newton , Jack A. Thorne

Abstract

Let $f$ be a non-CM Hecke eigenform of weight $k \geq 2$ . We give a new proof of some cases of Langlands functoriality for the automorphic representation $\pi$ associated to $f$ . More precisely, we prove the existence of the base change lifting, with respect to any totally real extension $F / \mathbb{Q}$ , of any symmetric power lifting of $\pi$ .

Keywords

non-abelian base change symmetric power lifting holomorphic modular forms Langlands functoriality Hecke eigenform totally real extension

Cite

@article{arxiv.2312.01774,
  title  = {Non-abelian base change for symmetric power liftings of holomorphic modular forms},
  author = {Laurent Clozel and James Newton and Jack A. Thorne},
  journal= {arXiv preprint arXiv:2312.01774},
  year   = {2024}
}

Comments

v2: new section 5 replaces reference to result not in the published version of [Tho24]. 26 pages

Non-abelian base change for symmetric power liftings of holomorphic modular forms

Abstract

Keywords

Cite

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