scholarly journals Eigenvalues of Hecke operators on Hilbert modular groups

2013 ◽  
Vol 17 (4) ◽  
pp. 729-758 ◽  
Author(s):  
Roelof W. Bruggeman ◽  
Roberto J. Miatello
Keyword(s):  
Hecke Operators ◽  
Modular Groups ◽  
Hilbert Modular

scholarly journals SYMMETRIES FOR BORCHERDS LIFTS ON HILBERT MODULAR GROUPS AND HIRZEBRUCH–ZAGIER DIVISORS

2013 ◽  
Vol 24 (08) ◽  
pp. 1350065 ◽  
Author(s):  
BERNHARD HEIM ◽  
ATSUSHI MURASE
Keyword(s):  
Modular Group ◽  
Quadratic Field ◽  
Hecke Operators ◽  
The Other ◽  
Real Quadratic Field ◽  
Hilbert Modular Group ◽  
Modular Groups ◽  
Hilbert Modular ◽  
The One ◽  
Real Quadratic

We show certain symmetries for Borcherds lifts on the Hilbert modular group over a real quadratic field. We give two different proofs, the one analytic and the other arithmetic. The latter proof yields an explicit description of the action of Hecke operators on Borcherds lifts.

scholarly journals Polygons and Hilbert modular groups

1989 ◽  
Vol 41 (4) ◽  
pp. 633-646 ◽  
Author(s):  
Ryoichi Kobayashi ◽  
Keiko Kushibiki ◽  
Isao Naruki
Keyword(s):  
Modular Groups ◽  
Hilbert Modular

scholarly journals A twisted topological trace formula for Hecke operators and liftings from symplectic to general linear groups

2011 ◽  
Vol 148 (1) ◽  
pp. 65-120 ◽  
Author(s):  
Uwe Weselmann
Keyword(s):  
Trace Formula ◽  
Hecke Operators ◽  
General Linear ◽  
Linear Groups ◽  
Arithmetic Subgroup ◽  
General Linear Groups ◽  
Locally Symmetric Space ◽  
Outer Automorphisms ◽  
Modular Groups ◽  
Endoscopic Group

AbstractFor the locally symmetric space X attached to an arithmetic subgroup of an algebraic group G of ℚ-rank r, we construct a compact manifold $\tilde X$ by gluing together 2r copies of the Borel–Serre compactification of X. We apply the classical Lefschetz fixed point formula to $\tilde X$ and get formulas for the traces of Hecke operators ℋ acting on the cohomology of X. We allow twistings of ℋ by outer automorphisms η of G. We stabilize this topological trace formula and compare it with the corresponding formula for an endoscopic group of the pair (G,η) . As an application, we deduce a weak lifting theorem for the lifting of automorphic representations from Siegel modular groups to general linear groups.

scholarly journals The large-scale geometry of Hilbert modular groups

1996 ◽  
Vol 44 (3) ◽  
pp. 435-478 ◽  
Author(s):  
Benson Farb ◽  
Richard Schwartz
Keyword(s):  
Large Scale ◽  
Large Scale Geometry ◽  
Modular Groups ◽  
Hilbert Modular

On Hilbert and quaternionic cusp forms

2006 ◽  
Vol 136 (1) ◽  
pp. 1-6
Author(s):  
A. Arenas
Keyword(s):  
Quaternion Algebra ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Natural Manner ◽  
Langlands Correspondence ◽  
Hilbert Modular

The aim of this paper is to determine in a natural manner the subspace of the space of Hilbert modular newforms of level n which correspond to eigenforms of an appropriate quaternion algebra, in the sense of having the same eigenvalues with respect to the corresponding Hecke operators. This study may be seen as a particular case of the Jacquet–Langlands correspondence.

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