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On the Areas of the Minimal Triangles in Veech Surfaces
Smillie and Weiss proved that the set of the areas of the minimal triangles of Veech surfaces with area 1 can be arranged as a strictly decreasing...
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Heat kernel approach for sup-norm bounds for cusp forms of integral and half-integral weight
In this article, using the heat kernel approach from Bouche (Asymptotic results for Hermitian line bundles over complex manifolds: The heat kernel...
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A relation of two metrics on a noncompact hyperbolic Riemann orbisurface
Jorgenson and Kramer (Compos Math 142:679–700,
2006 ) proved a certain key identity which relates the two natural metrics, namely the hyperbolic... -
On invariant function spaces H
Qp q (R)New function spaces, which generalize the classical Dirichlet space, BMOA or also the recently defined Q p space, are introduced on Riemann surfaces....
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Some characterizations of the integrable Teichmüller space
In this paper, we prove that the Bers projection of the integrable Teichmüller space is holomorphic. By using the Douady-Earle extension, we obtain...
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Upper estimates for hyperbolic metrics on subdomains
A result concerning upper estimates for hyperbolic metrics on subdomains is proved. The method of proof involves a standard technique based on the...
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On the Boundary Behaviour of Polymorphic Functions
Let Φ be a Fuchsian group acting on the unit disk D. This group may be infinitely generated and may have elliptic elements. A non-constant function f ...
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On Ramanujan relations between Eisenstein series
The Ramanujan relations between Eisenstein series can be interpreted as an ordinary differential equation in a parameter space of a family of...
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Shimura curves with many uniform dessins
A compact Riemann surface of genus g > 1 has different uniform dessins d’enfants of the same type if and only if its surface group S is contained in...
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Genus 2 Belyĭ surfaces with a unicellular uniform dessin
A bicoloured graph embedded in a compact oriented surface and dividing it into a union of simply connected components (faces) is known as a dessin...
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A series of coverings of the regular n-gon
We define an infinite series of translation coverings of Veech’s double-n-gon for odd n ≥ 5 which share the same Veech group. Additionally we give an...
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Corrigendum to “Note on zeros of the derivative of the Selberg zeta-function”
We correct constants in asymptotic formulas of our paper “Note on zeros of the derivative of the Selberg zeta-function”, Arch. Math. 91 (2008),...
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Isometries in hyperbolic spaces
Suppose that f : ℍ n → ℍ n ( n ⩾ 2) maps any r -dimensional hyperplane (1 ⩽ r < n ) into an r -dimensional hyperplane. In this paper, we prove that f is...
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On Beauville structures on the groups S n and A n
It is known that the symmetric group S n , for n ≥ 5, and the alternating group A n , for large n , admit a Beauville structure. In this paper we...
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A Characterization of Schur Multipliers Between Character-Automorphic Hardy Spaces
We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak...
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Note on zeros of the derivative of the Selberg zeta-function
Wenzhi Luo studied the distribution of nontrivial zeros of the derivatives of Selberg zeta-functions on cocompact hyperbolic surfaces, and obtained...
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The geometry at infinity of a hyperbolic Riemann surface of infinite type
We study geodesics on planar Riemann surfaces of infinite type having a single infinite end. Of particular interest is the class of geodesics that go...
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Riemann–Hilbert Problem for Automorphic Functions and the Schottky–Klein Prime Function
The construction of analogues of the Cauchy kernel is crucial for the solution of Riemann–Hilbert problems on compact Riemann surfaces. A formula for...
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Macbeaths infinite series of Hurwitz groups
In the present paper we will construct an infinite series of so-called Hurwitz groups. One possible way to describe Hurwitz groups is to define them...