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• Tags
  • #arithmetic-geometry/Langlands
• Refs:
  • #todo/add-references
• Links:
  • automorphy

automorphic L function

Setup:

• \(G\) a reductive group over a global field \(F\)
• \(\pi\) an automorphic representation of \(G\), which decomposes as \(\otimes_v \pi_v\) for \(v\in {\operatorname{Places}}(F)\).
• \(\psi\) a \({\mathbf{C}}{\hbox{-}}\)representation of the Langlands dual group \(G {}^{ \vee }\).

To this data there is an associated L function \(L(s, \pi, \psi)\). Should decompose as a product of local \(L\) functions at places \(v\) of \(F\).