scholarly journals Compact periods of Eisenstein series of orthogonal groups of rank one

2013 ◽  
Vol 62 (3) ◽  
pp. 869-890 ◽  
Author(s):  
Joao Pedro Boavida
Keyword(s):  
Eisenstein Series ◽  
Orthogonal Groups ◽  
Rank One

Poles ofL-functions and theta liftings for orthogonal groups

2009 ◽  
Vol 8 (4) ◽  
pp. 693-741 ◽  
Author(s):  
David Ginzburg ◽  
Dihua Jiang ◽  
David Soudry
Keyword(s):  
Eisenstein Series ◽  
Orthogonal Group ◽  
Symplectic Groups ◽  
Orthogonal Groups ◽  
Metaplectic Groups ◽  
Automorphic Representations ◽  
Domain Of Holomorphy ◽  
First Occurrence ◽  
Cuspidal Automorphic Representations

AbstractIn this paper, we prove that the first occurrence of global theta liftings from any orthogonal group to either symplectic groups or metaplectic groups can be characterized completely in terms of the location of poles of certain Eisenstein series. This extends the work of Kudla and Rallis and the work of Moeglin to all orthogonal groups. As applications, we obtain results about basic structures of cuspidal automorphic representations and the domain of holomorphy of twisted standardL-functions.

scholarly journals Symmetry breaking for representations of rank one orthogonal groups

2015 ◽  
Vol 238 (1126) ◽  
pp. 0-0 ◽  
Author(s):  
Toshiyuki Kobayashi ◽  
Birgit Speh
Keyword(s):  
Symmetry Breaking ◽  
Orthogonal Groups ◽  
Rank One

scholarly journals On the Siegel–Weil formula: The case of singular forms

2011 ◽  
Vol 147 (4) ◽  
pp. 1003-1021 ◽  
Author(s):  
Shunsuke Yamana
Keyword(s):  
Functional Equation ◽  
Eisenstein Series ◽  
Theta Function ◽  
Dual Pair ◽  
Orthogonal Groups ◽  
Special Value

AbstractFor the dual pair Sp(n)×O(m) with m≤n, we prove an identity between a special value of a certain Eisenstein series and the regularized integral of a theta function. The proof uses the functional equation of the Eisenstein series and the regularized Siegel–Weil formula for Sp(n)×O(2n+2−m). Analogous results for unitary and orthogonal groups are included.

Eisenstein series attached to lattices¶and modular forms on orthogonal groups

2001 ◽  
Vol 106 (4) ◽  
pp. 443-459 ◽  
Author(s):  
Jan Hendrik Bruinier ◽  
Michael Kuss
Keyword(s):  
Eisenstein Series ◽  
Modular Forms ◽  
Orthogonal Groups

Rank One Reducibility for Metaplectic Groups via Theta Correspondence

2011 ◽  
Vol 63 (3) ◽  
pp. 591-615 ◽  
Author(s):  
Marcela Hanzer ◽  
Goran Muić
Keyword(s):  
Parabolic Subgroups ◽  
Orthogonal Groups ◽  
Metaplectic Groups ◽  
Theta Correspondence ◽  
Rank One ◽  
Maximal Parabolic Subgroups ◽  
Cuspidal Representations

Abstract We calculate reducibility for the representations of metaplectic groups induced from cuspidal representations of maximal parabolic subgroups via theta correspondence, in terms of the analogous representations of the odd orthogonal groups. We also describe the lifts of all relevant subquotients.

Special representations of rank one orthogonal groups

1988 ◽  
Vol 64 (3) ◽  
pp. 276-314 ◽  
Author(s):  
Ilya I. Piatetski-Shapiro ◽  
David Soudry
Keyword(s):  
Orthogonal Groups ◽  
Rank One
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