Tags: ? Refs: automorphic form
Automorphic representation
Cuspidal representation
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automorphic representation
- files without tags
- automorphic form
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automorphic L function
\(\pi\) an automorphic representation of \(G\), which decomposes as \(\otimes_v \pi_v\) for \(v\in {\operatorname{Places}}(F)\).
- admissible representation
- L function
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Beuzart-Plessis, On the spectral decomposition of the Jacquet-Rallis trace formula and the Gan-Gross-Prasad conjecture for unitary groups
Look at automorphic cuspidal representations to \(\operatorname{PGL}_2({ \mathbf{F} })\) for \({ \mathbf{F} }\) a number field.
Theorem: from the Langlands philosophy. There is a Hermitian form and a cuspidal representation in the same L packet where \(P\) is nonvanishing .
