The local converse theorem for SO ( 2 n + 1 ) and applications

  title={The local converse theorem for SO ( 2 n + 1 ) and applications},
  author={Dihua Jiang and David Soudry},
In this paper we characterize irreducible generic representations of SO2n+1(k) (where k is a p-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic cuspidal automorphic representations of SO2n+1(A) (where A is the ring of adeles of a number field) are equivalent if their local components are equivalent at almost all local places (the Rigidity Theorem); and prove the Local Langlands Reciprocity Conjecture for… CONTINUE READING
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