Automorphic L-function

introduction

• an automorphic L-function is a function \(L(s,\pi,r)\)
  • complex variable \(s\),
  • associated to an automorphic form \(\pi\) of a reductive group \(G\) over a global field
  • a finite-dimensional complex representation \(r\) of the Langlands dual group \(^LG\) of \(G\),
• They were introduced by Langlands (1967, 1970, 1971)
• generalizing the Dirichlet \(L\)-series of a Dirichlet character and the Mellin transform of a modular form

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• ID : Q4826697