# Multiple prime covers of the riemann sphere

Open Mathematics (2005)

- Volume: 3, Issue: 2, page 260-272
- ISSN: 2391-5455

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topAaron Wootton. "Multiple prime covers of the riemann sphere." Open Mathematics 3.2 (2005): 260-272. <http://eudml.org/doc/268774>.

@article{AaronWootton2005,

abstract = {A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.},

author = {Aaron Wootton},

journal = {Open Mathematics},

keywords = {14H30; 14H37; 30F10; 30F60; 20H10},

language = {eng},

number = {2},

pages = {260-272},

title = {Multiple prime covers of the riemann sphere},

url = {http://eudml.org/doc/268774},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Aaron Wootton

TI - Multiple prime covers of the riemann sphere

JO - Open Mathematics

PY - 2005

VL - 3

IS - 2

SP - 260

EP - 272

AB - A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.

LA - eng

KW - 14H30; 14H37; 30F10; 30F60; 20H10

UR - http://eudml.org/doc/268774

ER -

## References

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- [2] R.D.M. Accola: “Riemann Surfaces with Automorphism Groups Admitting Partitions”, Proc. Amer. Math. Soc., Vol. 21, (1969), pp. 477–482. http://dx.doi.org/10.2307/2037029 Zbl0174.37401
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- [5] A.M. Macbeath: “On a Theorem of Hurwitz”, Proceedings of the Glasgow Mathematical Association, Vol. 5, (1961), pp. 90–96. http://dx.doi.org/10.1017/S2040618500034365 Zbl0134.16603
- [6] B. Maskit: “On Poincaré's Theorem for Fundamental Polygons”, Advances in Mathematics, (1971), Vol. 7, pp. 219–230. http://dx.doi.org/10.1016/S0001-8708(71)80003-8 Zbl0223.30008
- [7] D. Singerman: “Finitely Maximal Fuchsian Groups”, J. London Math. Soc., Vol. 2 (6), (1972), pp. 29–38. Zbl0251.20052
- [8] A. Wootton: “Non-Normal Belyî p-gonal Surfaces”, In: Computational Aspects of Algebraic Curves, Lect. Notes in Comp., (2005), to appear.
- [9] A. Wootton: “Defining Algebraic Polynomials for Cyclic Prime Covers of the Riemann Sphere”, Dissertation, (2004).

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