Trigonal modular curves

• Autorzy: Yuji Hasegawa , Mahoro Shimura
• Języki publikacji: EN

Kategorie tematyczne

• 14H25: Arithmetic ground fields
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 11F11: Holomorphic modular forms of integral weight
• 14E20: Coverings
• 11F03: Modular and automorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 88
• Numer: 2
• Strony: 129-140

Daty

wydano

1999

otrzymano

1997-07-15

poprawiono

1998-10-23

Twórcy

autor

Yuji Hasegawa

• Department of Mathematics, Waseda University, 3-4-1, Okubo Shinjuku-ku, Tokyo, 169-8555 Japan

autor

Mahoro Shimura

• Department of Mathematics, Waseda University, 3-4-1, Okubo Shinjuku-ku, Tokyo, 169-8555 Japan

Bibliografia

• [1] E. Arbarello et al., Geometry of Algebraic Curves, Vol. I, Grundlehren Math. Wiss. 267, Springer, 1985.
• [2] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160.
• [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] M. Furumoto and Y. Hasegawa, Hyperelliptic quotients of modular curves X₀(N), Tokyo J. Math., to appear.
• [5] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, 1977.
• [6] H. Hijikata, Explicit formula of the traces of Hecke operators for Γ₀(N), J. Math. Soc. Japan 26 (1974), 56-82.
• [7] J. Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math. 81 (1959), 561-577.
• [8] S. L. Kleiman and D. Laksov, Another proof of the existence of special divisors, Acta Math. 132 (1974), 163-176.
• [9] F. Momose, p-torsion points on elliptic curves defined over quadratic fields, Nagoya Math. J. 96 (1984), 139-165.
• [10] F. Momose and S. Yamada, Another estimate of the level of d-gonal modular curves, preprint.
• [11] M. Newman, Conjugacy, genus, and class number, Math. Ann. 196 (1972), 198-217.
• [12] K. V. Nguyen and M.-H. Saito, D-gonality of modular curves and bounding torsions, preprint.
• [13] A. P. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462.
• [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] J. P. Serre, Local Fields, Grad. Texts in Math. 67, Springer, 1979.
• [16] M. Shimura, Defining equations of modular curves X₀(N), Tokyo J. Math. 18 (1995), 443-456.
• [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).