Geodesic
A Functional Equation for Degree two Local Factors
Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 355-371

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DOI

We show that the Fourier transforms of the admissible irreducible representations of the group GL2 over a nonarchimedian local field F are characterized by a functional equation (MF). We also prove that the functions satisfying (MF) and having at most one pole are exactly the Fourier transforms of the irreducible representations of the quaternion group H over F. The Jacquet-Langlands correspondence between irreducible representations of H and discrete series of GL2 then follows immediately from our criteria.
DOI : 10.4153/CMB-1985-043-0
Mots-clés : 12B27, 12B30 
Gérardin, Paul; Li, Wen-Ch'ing Winnie. A Functional Equation for Degree two Local Factors. Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 355-371. doi: 10.4153/CMB-1985-043-0
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     author = {G\'erardin, Paul and Li, Wen-Ch'ing Winnie},
     title = {A {Functional} {Equation} for {Degree} two {Local} {Factors}},
     journal = {Canadian mathematical bulletin},
     pages = {355--371},
     year = {1985},
     volume = {28},
     number = {3},
     doi = {10.4153/CMB-1985-043-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-043-0/}
}
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