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Genus Zero Actions on Riemann Surfaces  [PDF]
Sadok Kallel,Denis Sjerve
Mathematics , 1999,
Abstract: In this paper we determine all finite groups G that can act on some compact Riemann surface M with the property that if H is any non-trivial subgroup of G, then the orbit surface M/H is the Riemann sphere. The idea is to look at the induced action on the vector space of holomorphic differentials on M (in the positive genus case) and then use the old-known (Wolf) classification of groups admitting fixed point-free linear actions. A description of the corresponding group actions is given in terms of Fuchsian representations.
A bound for the number of automorphisms of an arithmetic Riemann surface  [PDF]
M. Belolipetsky,G. A. Jones
Mathematics , 2003,
Abstract: We show that for every g > 1 there is a compact arithmetic Riemann surface of genus g with at least 4(g-1) automorphisms, and that this lower bound is attained by infinitely many genera, the smallest being 24.
On symplectic vortex equations over a compact orbifold Riemann surface  [PDF]
Hironori Sakai
Mathematics , 2012,
Abstract: Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack. After that we define symplectic vortex equations over a compact orbifold Riemann surface. We also discuss the moduli space of solutions to the equations for linear actions of the circle group on the complex plane.
Topological Classification of Conformal Actions on -Hyperelliptic Riemann Surfaces
Ewa Tyszkowska
International Journal of Mathematics and Mathematical Sciences , 2007, DOI: 10.1155/2007/47839
Abstract: A compact Riemann surface X of genus g>1 is said to be p-hyperelliptic if X admits a conformal involution ρ, for which X/ρ is an orbifold of genus p. If in addition X is q-hyperelliptic, then we say that X is pq-hyperelliptic. Here we study conformal actions on pq-hyperelliptic Riemann surfaces with central p- and q-hyperelliptic involutions.
On the lower bound estimates of sections of the canonical bundle over a Riemann surface  [PDF]
Zhiqin Lu
Mathematics , 1999,
Abstract: In this paper, we give some estimates of the sum of the square norm of the sections of the pluricanonical bundles over a Riemann surface with genus greater than 2 and Gauss curvature (-1). Using these estimate, we give a uniform estimate of the corona problem on Riemann surfaces.
A lower bound in an approximation problem involving the zeros of the Riemann zeta function  [PDF]
Jean-Francois Burnol
Mathematics , 2001, DOI: 10.1006/aima.2001.2066
Abstract: We slightly improve the lower bound of Baez-Duarte, Balazard, Landreau and Saias in the Nyman-Beurling formulation of the Riemann Hypothesis as an approximation problem. We construct Hilbert space vectors which could prove useful in the context of the so-called `Hilbert-Polya idea'.
Topological classifcation of conformal actions on p-hyperelliptic and (q,n)-gonal Riemann surfaces
Ewa Tyszkowska
Opuscula Mathematica , 2009,
Abstract: A compact Riemann surface $X$ of genus $g > 1$ is said to be $p$-hyperelliptic if $X$ admits a conformal involution $\rho$ for which $X / \rho$ has genus $p$. A conformal automorphism $\delta$ of prime order $n$ such that $X / \delta$ has genus $q$ is called a $(q,n)$-gonal automorphism. Here we study conformal actions on $p$-hyperelliptic Riemann surface with $(q,n)$-gonal automorphism.
The resultant on compact Riemann surfaces  [PDF]
B. Gustafsson,V. Tkachev
Mathematics , 2007, DOI: 10.1007/s00220-008-0622-2
Abstract: We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.
A Lower Bound of the First Dirichlet Eigenvalue of a Compact Manifold with Positive Ricci Curvature  [PDF]
Jun Ling
Mathematics , 2004,
Abstract: We give a new estimate on the lower bound for the first Dirichlet eigenvalue for a compact manifold with positive Ricci curvature in terms of the in-diameter and the lower bound of the Ricci curvature. The result improves the previous estimates.
A lower bound for the minimum deviation of the Chebyshev polynomial on a compact real set  [PDF]
Klaus Schiefermayr
Mathematics , 2013,
Abstract: In this paper, we give a sharp lower bound for the minimum deviation of the Chebyshev polynomial on a compact subset of the real line in terms of the corresponding logarithmic capacity. Especially if the set is the union of several real intervals, together with a lower bound for the logarithmic capacity derived recently by A.Yu.\,Solynin, one has a lower bound for the minimum deviation in terms of elementary functions of the endpoints of the intervals. In addition, analogous results for compact subsets of the unit circle are given.
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