Weierstrass Points on Compact Riemann Surfaces

1971 ◽  
Vol s2-3 (4) ◽  
pp. 722-724 ◽  
Author(s):  
C. MacLachlan
Keyword(s):  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

scholarly journals Automorphisms with fixed points and Weierstrass points of compact Riemann surfaces

1993 ◽  
Vol 17 (1) ◽  
pp. 221-249 ◽  
Author(s):  
Katsuaki Yoshida
Keyword(s):  
Fixed Points ◽  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

scholarly journals On Weierstrass points of non-hyperelliptic compact Riemann surfaces of genus three

1977 ◽  
Vol 7 (3) ◽  
pp. 743-768 ◽  
Author(s):  
Akikazu Kuribayashi ◽  
Kaname Komiya
Keyword(s):  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

scholarly journals Weierstrass points on compact Riemann surfaces with nontrivial automorphisms

1981 ◽  
Vol 33 (2) ◽  
pp. 235-246 ◽  
Author(s):  
Nobumasa TAKIGAWA
Keyword(s):  
Riemann Surfaces ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

On Weierstrass Points of a Family of Quartic Curves

2015 ◽  
Vol 25 (14) ◽  
pp. 1540027
Author(s):  
Saleem Mohammed ◽  
Badr Eslam
Keyword(s):  
Finite Group ◽  
Riemann Surfaces ◽  
Group Actions ◽  
Finite Group Actions ◽  
Weierstrass Points ◽  
The Family ◽  
Compact Riemann Surfaces ◽  
Quartic Curves

The aim of this paper is to investigate properties of the Weierstrass points on the family of compact Riemann surfaces [Formula: see text], where [Formula: see text] and [Formula: see text] are parameters such that [Formula: see text] and [Formula: see text] by using finite group actions on this family. Furthermore, the geometry of these points is discussed.

scholarly journals Weierstrass points on modular curves X0(N) fixed by the Atkin–Lehner involutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Bojakli ◽  
Hasan Sankari
Keyword(s):  
Riemann Surfaces ◽  
Coding Theory ◽  
Design Methodology ◽  
Automorphism Groups ◽  
Group Structure ◽  
Weierstrass Point ◽  
Algebraic Number Theory ◽  
Content Type ◽  
Weierstrass Points ◽  
Compact Riemann Surfaces

PurposeThe authors have determined whether the points fixed by all the full and the partial Atkin–Lehner involutions WQ on X0(N) for N ≤ 50 are Weierstrass points or not.Design/methodology/approachThe design is by using Lawittes's and Schoeneberg's theorems.FindingsFinding all Weierstrass points on X0(N) fixed by some Atkin–Lehner involutions. Besides, the authors have listed them in a table.Originality/valueThe Weierstrass points have played an important role in algebra. For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. Finally, the set of Weierstrass points is useful in studying arithmetic and geometric properties of X0(N).

A Hodge theoretic projective structure on compact Riemann surfaces

2021 ◽  
Vol 149 ◽  
pp. 1-27
Author(s):  
Indranil Biswas ◽  
Elisabetta Colombo ◽  
Paola Frediani ◽  
Gian Pietro Pirola
Keyword(s):  
Riemann Surfaces ◽  
Projective Structure ◽  
Compact Riemann Surfaces

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

Factorization of univalent analytic functions on compact Riemann surfaces with boundary

1993 ◽  
Vol 63 (2) ◽  
pp. 275-290
Author(s):  
S. Ya. Khavinson
Keyword(s):  
Analytic Functions ◽  
Riemann Surfaces ◽  
Compact Riemann Surfaces
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