scholarly journals Selberg type zeta function for the Hilbert modular group of a real quadratic field

2012 ◽  
Vol 88 (9) ◽  
pp. 145-148 ◽  
Author(s):  
Yasuro Gon
Keyword(s):  
Zeta Function ◽  
Modular Group ◽  
Quadratic Field ◽  
Real Quadratic Field ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Real Quadratic

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.

RESTRICTIONS OF HILBERT MODULAR FORMS

2009 ◽  
Vol 05 (01) ◽  
pp. 67-80
Author(s):  
NAJIB OULED AZAIEZ
Keyword(s):  
Modular Forms ◽  
Modular Group ◽  
Quadratic Field ◽  
Hilbert Modular Forms ◽  
Real Quadratic Field ◽  
Modular Surface ◽  
Modular Curve ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Real Quadratic

Let Γ ⊂ PSL (2, ℝ) be a discrete and finite covolume subgroup. We suppose that the modular curve [Formula: see text] is "embedded" in a Hilbert modular surface [Formula: see text], where ΓK is the Hilbert modular group associated to a real quadratic field K. We define a sequence of restrictions (ρn)n∈ℕ of Hilbert modular forms for ΓK to modular forms for Γ. We denote by Mk1, k2(ΓK) the space of Hilbert modular forms of weight (k1, k2) for ΓK. We prove that ∑n∈ℕ ∑k1, k2∈ℕ ρn(Mk1, k2(ΓK)) is a subalgebra closed under Rankin–Cohen brackets of the algebra ⊕k∈ℕ Mk(Γ) of modular forms for Γ.

MINIMA OF BINARY INDEFINITE HERMITIAN FORMS

2010 ◽  
Vol 06 (02) ◽  
pp. 411-435 ◽  
Author(s):  
L. YA. VULAKH
Keyword(s):  
Modular Group ◽  
Quadratic Field ◽  
Three Dimensional ◽  
Hermitian Forms ◽  
Space Model ◽  
Continuous Parameter ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Group B

Classification of binary indefinite primitive Hermitian forms modulo the action of the extended Bianchi group (or Hilbert modular group) Bd is given. When the discriminant of the quadratic field [Formula: see text] (and d) is negative, the results obtained can be applied to classify the maximal non-elementary Fuchsian subgroups of Bd, and to find the Hermitian points in the Markov spectrum of Bd. If ν is a Hermitian point in the spectrum, then there is a set of extremal geodesics in H3, the upper half-space model of the three-dimensional hyperbolic space, with diameter 1/ν, which depends on one continuous parameter.

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