The Action of the Modular Group on the Fundamental Domain

2008 ◽  
Keyword(s):  
Fundamental Domain ◽  
Modular Group

ZERO DISTRIBUTION AND DECAY AT INFINITY OF DRINFELD MODULAR COEFFICIENT FORMS

2011 ◽  
Vol 07 (03) ◽  
pp. 671-693 ◽  
Author(s):  
ERNST-ULRICH GEKELER
Keyword(s):  
Half Plane ◽  
Modular Forms ◽  
Fundamental Domain ◽  
Modular Group ◽  
Zero Distribution ◽  
Upper Half Plane

Let Γ = GL (2, 𝔽q[T]) be the Drinfeld modular group, which acts on the rigid analytic upper half-plane Ω. We determine the zeroes of the coefficient modular forms aℓk on the standard fundamental domain [Formula: see text] for Γ on Ω, along with the dependence of |aℓk(z)| on [Formula: see text].

A minimal volume arithmetic cusped complex hyperbolic orbifold

2010 ◽  
Vol 150 (2) ◽  
pp. 313-342 ◽  
Author(s):  
TIEHONG ZHAO
Keyword(s):  
Fundamental Domain ◽  
Modular Group ◽  
Minimal Volume ◽  
Hyperbolic Orbifold ◽  
Group A ◽  
Picard Modular Group

AbstractThe sister of Eisenstein–Picard modular group is described explicitly in [10], whose quotient is a noncompact arithmetic complex hyperbolic 2-orbifold of minimal volume (see [16]). We give a construction of a fundamental domain for this group. A presentation of that lattice can be obtained from that construction, which relates to one of Mostow's lattices.

scholarly journals A zeta function connected with the eigenvalues of the Laplace-Beltrami operator on the fundamental domain of the modular group

1984 ◽  
Vol 96 ◽  
pp. 167-174 ◽  
Author(s):  
Akio Fujii
Keyword(s):  
Zeta Function ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Fundamental Domain ◽  
Modular Group ◽  
Beltrami Operator

Let ; … run over the eigenvalues of the discrete spectrum of the Laplace-Beltrami operator on L2(H/yΓ), where H is the upper half of the complex plane and we take Γ = PSL(2, Z). It is well known that Let a be a positive number. Here we are concerned with the zeta function defined by

scholarly journals Forests of complex numbers

2016 ◽  
Vol 13 (01) ◽  
pp. 15-25 ◽  
Author(s):  
Melvyn B. Nathanson
Keyword(s):  
Binary Tree ◽  
Fundamental Domain ◽  
Modular Group ◽  
Rational Numbers ◽  
Complex Numbers ◽  
Positive Integers ◽  
Positive Complex

The Calkin–Wilf tree is an infinite binary tree whose vertices are the positive rational numbers. Each number occurs in the tree exactly once and in the form [Formula: see text], where [Formula: see text] and [Formula: see text] are relatively prime positive integers. In this paper, certain subsemigroups of the modular group are used to construct similar trees in the set [Formula: see text] of positive complex numbers. Associated to each subsemigroup is a forest of trees that partitions [Formula: see text]. The fundamental domain and the set of cusps of the subsemigroup are defined and computed.

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