SYMMETRIC POWER FUNCTORIALITY FOR HOLOMORPHIC MODULAR FORMS
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Resumen del artículo
This paper proves the automorphy of symmetric power liftings for all n ≥ 1 for cuspidal Hecke eigenforms of level 1 and weight k > 2. The result also applies to a more general class of eigenforms, including those associated with semistable elliptic curves, significantly advancing Langlands's functoriality principle.
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Scientists found that special math patterns can be used to create new, related patterns, and these new ones are also very neat and follow the same rules. This helps crack a huge math puzzle called Langlands's principle.
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Explicación de la calificación
The paper makes significant contributions to Langlands's functoriality principle by establishing the automorphy of symmetric power liftings for a wider class of modular forms, including those associated with semistable elliptic curves. The approach, combining Galois deformation theory, p-adic families, and eigenvarieties, is innovative and robust, thus earning a rating of 4 despite its technical complexity and specialized focus.
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