SYMMETRIC POWER FUNCTORIALITY FOR HOLOMORPHIC MODULAR FORMS
Overview
Paper Summary
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.
Explain Like I'm Five
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.
Possible Conflicts of Interest
None identified
Identified Limitations
Rating Explanation
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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