Đề tài " The local converse theorem for SO(2n+1) and applications "
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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 generic supercuspidal representations of SO2n+1 (k). ...
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