On the theta constant of genus 8 and Hilbert modular groups over certain cyclic biquadratic fields

1987 ◽  
Vol 278 (1-4) ◽  
pp. 185-192
Author(s):  
Hidehisa Naganuma
Keyword(s):  
Modular Groups ◽  
Hilbert Modular ◽  
Biquadratic Fields

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 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

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 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 Density results for automorphic forms on Hilbert modular groups II

2010 ◽  
Vol 362 (07) ◽  
pp. 3841-3881
Author(s):  
Roelof W. Bruggeman ◽  
Roberto J. Miatello
Keyword(s):  
Automorphic Forms ◽  
Modular Groups ◽  
Hilbert Modular ◽  
Density Results

scholarly journals Higher order Dehn functions for horospheres in products of Hadamard spaces

2019 ◽  
Vol 19 (1) ◽  
pp. 15-20
Author(s):  
Gabriele Link
Keyword(s):  
Symmetric Spaces ◽  
Higher Order ◽  
Regular Boundary ◽  
Dehn Functions ◽  
Modular Groups ◽  
Hilbert Modular ◽  
Rank One ◽  
Riemannian Symmetric Spaces ◽  
Geodesically Complete ◽  
Nagata Dimension

Abstract Let X be a product of r locally compact and geodesically complete Hadamard spaces. We prove that the horospheres in X centered at regular boundary points of X are Lipschitz-(r − 2)-connected. If X has finite Assouad–Nagata dimension, then using the filling construction by R. Young in [10] this gives sharp bounds on higher order Dehn functions for such horospheres. Moreover, if Γ ⊂ Is(X) is a lattice acting cocompactly on X minus a union of disjoint horoballs, then we get a sharp bound on higher order Dehn functions for Γ. We deduce that apart from the Hilbert modular groups already considered by R. Young, every irreducible ℚ-rank one lattice acting on a product of r Riemannian symmetric spaces of the noncompact type is undistorted up to dimension r−1 and has k-th order Dehn function asymptotic to V(k+1)/k for all k ≤ r − 2.

scholarly journals Density results for automorphic forms on Hilbert modular groups

2003 ◽  
Vol 13 (4) ◽  
pp. 681-719 ◽  
Author(s):  
R.W. Bruggeman ◽  
R.J. Miatello ◽  
I. Pacharoni
Keyword(s):  
Automorphic Forms ◽  
Modular Groups ◽  
Hilbert Modular ◽  
Density Results

scholarly journals Non-combability of Hilbert modular groups

1995 ◽  
Vol 3 (2) ◽  
pp. 223-251 ◽  
Author(s):  
Toshiaki Hattori
Keyword(s):  
Modular Groups ◽  
Hilbert Modular
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