Geodesic
The local converse theorem for ${\rm SO}(2n+1)$ and applications
Dihua Jiang1 ; David Soudry2
1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States
2 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Annals of mathematics, Tome 157 (2003) no. 3, pp. 743-806.

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In this paper we characterize irreducible generic representations of ${\rm SO}_{2n+1}(k)$ (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 ${\rm SO}_{2n+1}({\Bbb A})$ (where ${\Bbb A}$ 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 ${\rm SO}_{2n+1}(k)$.
DOI : 10.4007/annals.2003.157.743

Dihua Jiang 1 ; David Soudry 2

1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States
2 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel 
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Dihua Jiang; David Soudry. The local converse theorem for ${\rm SO}(2n+1)$ and applications. Annals of mathematics, Tome 157 (2003) no. 3, pp. 743-806. doi : 10.4007/annals.2003.157.743. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.743/

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