Trigonal modular curves

Yuji Hasegawa; Mahoro Shimura

Acta Arithmetica (1999)

  • Volume: 88, Issue: 2, page 129-140
  • ISSN: 0065-1036

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Yuji Hasegawa, and Mahoro Shimura. "Trigonal modular curves." Acta Arithmetica 88.2 (1999): 129-140. <http://eudml.org/doc/207234>.

@article{YujiHasegawa1999,
author = {Yuji Hasegawa, Mahoro Shimura},
journal = {Acta Arithmetica},
keywords = {modular curve; modular form; gonality},
language = {eng},
number = {2},
pages = {129-140},
title = {Trigonal modular curves},
url = {http://eudml.org/doc/207234},
volume = {88},
year = {1999},
}

TY - JOUR
AU - Yuji Hasegawa
AU - Mahoro Shimura
TI - Trigonal modular curves
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 2
SP - 129
EP - 140
LA - eng
KW - modular curve; modular form; gonality
UR - http://eudml.org/doc/207234
ER -

References

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  1. [1] E. Arbarello et al., Geometry of Algebraic Curves, Vol. I, Grundlehren Math. Wiss. 267, Springer, 1985. 
  2. [2] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160. 
  3. [3] A. O. L. Atkin and D. J. Tingley, Numerical tables on elliptic curves, in: Modular Functions of One Variable IV, B. Birch and W. Kuyk (eds.), Lecture Notes in Math. 476, Springer, 1975, 74-144. 
  4. [4] M. Furumoto and Y. Hasegawa, Hyperelliptic quotients of modular curves X₀(N), Tokyo J. Math., to appear. Zbl0947.11019
  5. [5] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, 1977. 
  6. [6] H. Hijikata, Explicit formula of the traces of Hecke operators for Γ₀(N), J. Math. Soc. Japan 26 (1974), 56-82. Zbl0266.12009
  7. [7] J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math. 81 (1959), 561-577. Zbl0093.04502
  8. [8] S. L. Kleiman and D. Laksov, Another proof of the existence of special divisors, Acta Math. 132 (1974), 163-176. Zbl0286.14005
  9. [9] F. Momose, p-torsion points on elliptic curves defined over quadratic fields, Nagoya Math. J. 96 (1984), 139-165. Zbl0578.14021
  10. [10] F. Momose and S. Yamada, Another estimate of the level of d-gonal modular curves, preprint. 
  11. [11] M. Newman, Conjugacy, genus, and class number, Math. Ann. 196 (1972), 198-217. Zbl0221.10030
  12. [12] K. V. Nguyen and M.-H. Saito, D-gonality of modular curves and bounding torsions, preprint. 
  13. [13] A. P. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462. Zbl0314.10018
  14. [14] B. Saint-Donat, On Petri's analysis of the linear system of quadrics through a canonical curve, Math. Ann. 206 (1973), 157-175. 
  15. [15] J. P. Serre, Local Fields, Grad. Texts in Math. 67, Springer, 1979. 
  16. [16] M. Shimura, Defining equations of modular curves X₀(N), Tokyo J. Math. 18 (1995), 443-456. Zbl0865.11052
  17. [17] P. G. Zograf, Small eigenvalues of automorphic Laplacians in spaces of cusp forms, in: Automorphic Functions and Number Theory, II, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1984), 157-168 (in Russian). Zbl0536.10018

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