Equations of hyperelliptic modular curves

Josep Gonzalez Rovira

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 4, page 779-795
  • ISSN: 0373-0956

Abstract

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We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.

How to cite

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Rovira, Josep Gonzalez. "Equations of hyperelliptic modular curves." Annales de l'institut Fourier 41.4 (1991): 779-795. <http://eudml.org/doc/74938>.

@article{Rovira1991,
abstract = {We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.},
author = {Rovira, Josep Gonzalez},
journal = {Annales de l'institut Fourier},
keywords = {equations of hyperelliptic modular curves},
language = {eng},
number = {4},
pages = {779-795},
publisher = {Association des Annales de l'Institut Fourier},
title = {Equations of hyperelliptic modular curves},
url = {http://eudml.org/doc/74938},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Rovira, Josep Gonzalez
TI - Equations of hyperelliptic modular curves
JO - Annales de l'institut Fourier
PY - 1991
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 4
SP - 779
EP - 795
AB - We compute, in a unified way, the equations of all hyperelliptic modular curves. The main tool is provided by a class of modular functions introduced by Newman in 1957. The method uses the action of the hyperelliptic involution on the cusps.
LA - eng
KW - equations of hyperelliptic modular curves
UR - http://eudml.org/doc/74938
ER -

References

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  1. [ALe] A. O. ATKIN, J. LEHNER, Hecke Operators on Г0(m), Math. Ann., 185 (1970), 134-160. Zbl0177.34901MR42 #3022
  2. [B] B. J. BIRCH, Some calculations of modulars relations, in "Modular Functions of One Variable I", Springer Lecture Notes, 320, 175-186. Zbl0261.10019MR48 #10984
  3. [F] R. FRICKE, "Die elliptischen Funktionen und ihre Anwendungen, II", Teubner (1922). Zbl48.0432.01JFM48.0432.01
  4. [K] P. G. KLUIT, On the Normalizer of Г0(N), in "Modular Functions of One Variable V". Springer Lecture Notes 601. Zbl0355.10020MR58 #513
  5. [LeN] J. LEHNER, M. NEWMAN, Weierstrass points of Г0(N), Ann. of Math., 79 (1964), 360-368. Zbl0124.29203MR28 #5045
  6. [Li] G. LIGOZAT, Courbes modulaires de genre 1, Bull. Soc. Math. France, Mémoire, 43 (1975). Zbl0322.14011MR54 #5121
  7. [MS] B. MAZUR, Swinnerton-Dyer, P : Arithmetic of Weil Curves, Inventiones Math., 25 (1974), 1-61. Zbl0281.14016
  8. [N1] M. NEWMAN, Construction and application of a class of modular functions, Proceed. of London Math. Soc., (1957), 334-350. Zbl0097.28701MR19,953c
  9. [N2] M. NEWMAN, Construction and application of a class of modular functions (II), Proceed. of London Math. Soc., (1959), 373-387. Zbl0178.43001MR21 #6354
  10. [O1] A. P. OGG, Hyperelliptic Modular Curves, Bull. Soc. Math. France, 102 (1974), 449-462. Zbl0314.10018MR51 #514
  11. [O2] A. P. OGG, On the Weierstarss points of X0(N), Illinois J. of Math., Vol. 22 (1978), 31-35. Zbl0374.14005MR57 #3136
  12. [R] E. REYSSAT, Quelques Aspects des Surfaces de Riemann, Birkhäusser, 1989. Zbl0689.30001MR90k:30085

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