Symmetric power functoriality for holomorphic modular forms

James Newton; Jack A. Thorne

doi:10.1007/s10240-021-00127-3

Article

Symmetric power functoriality for holomorphic modular forms

James Newton; Jack A. Thorne

Publications Mathématiques de l'IHÉS, Volume 134 (2021), pp. 1-116

Abstract

Let $f$ be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric power lifting ${Sym}^{n} f$ for every $n \geq 1$ .

We establish the same result for a more general class of cuspidal Hecke eigenforms, including all those associated to semistable elliptic curves over $𝐐$ .

Received: 2020-07-17
Accepted: 2021-09-25
Online First: 2021-10-15
Published online: 2021-12-07

MR Zbl

DOI: 10.1007/s10240-021-00127-3

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     author = {James Newton and Jack A. Thorne},
     title = {Symmetric power functoriality for holomorphic modular forms},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--116},
     year = {2021},
     publisher = {Springer International Publishing},
     address = {Cham},
     volume = {134},
     doi = {10.1007/s10240-021-00127-3},
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James Newton; Jack A. Thorne. Symmetric power functoriality for holomorphic modular forms. Publications Mathématiques de l'IHÉS, Volume 134 (2021), pp. 1-116. doi: 10.1007/s10240-021-00127-3

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