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Publications mathématiques de l IHÉS

Let $f$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>f</mml:mi> </mml:math> be a cuspidal Hecke eigenform without complex multiplication. We prove the automorphy of the symmetric power lifting $\operatorname{Sym}^{n} f$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mo>Sym</mml:mo> <mml:mi>n</mml:mi> </mml:msup> <mml:mi>f</mml:mi> </mml:math> for every $n \geq 1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> </mml:math> .

Symmetric power functoriality for holomorphic modular forms, II