Hyperelliptic modular curves $X*_0(N)$

• Autorzy: Yuji Hasegawa
• Języki publikacji: EN

Kategorie tematyczne

• 14H45: Special curves and curves of low genus
• 14H25: Arithmetic ground fields
• 11F06: Structure of modular groups and generalizations; arithmetic groups
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 14G05: Rational points
• 11F11: Holomorphic modular forms of integral weight

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 81
• Numer: 4
• Strony: 369-385

Daty

wydano

1997

otrzymano

1996-11-22

poprawiono

1997-02-21

Twórcy

autor

Yuji Hasegawa

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

Bibliografia

• [1] A. O. L. Atkin and J. Lehner, Hecke operators on $Γ_0(m)$, Math. Ann. 185 (1970), 134-160.
• [2] 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, Berlin, 1975, 74-144.
• [3] P. Deligne et M. Rapoport, Les schémas de modules de courbes elliptiques, in: Modular Functions of One Variable II, P. Deligne and W. Kuyk (eds.), Lecture Notes in Math. 349, Springer, Berlin, 1973, 143-316.
• [4] R. Fricke, Die Elliptischen Funktionen und ihre Anwendungen, Teubner, Leipzig and Berlin, 1916.
• [5] Y. Hasegawa, Table of quotient curves of modular curves $X_0(N)$ with genus 2, Proc. Japan Acad. Ser. A 71 (1995), 235-239.
• [6] Y. Hasegawa, Modular abelian surfaces and hyperelliptic curves of genus two, preprint.
• [7] Y. Hasegawa and K. Hashimoto, Hyperelliptic modular curves $X*_0(N)$ with square-free levels, Acta Arith. 77 (1996), 179-193.
• [8] H. Hijikata, Explicit formula of the traces of Hecke operators for $Γ_0(N)$, J. Math. Soc. Japan 26 (1974), 56-82.
• [9] P. G. Kluit, Hecke operators on Γ*(N) and their traces, Dissertation of Vrije Universiteit, Amsterdam, 1979.
• [10] J. Lehner and M. Newman, Weierstrass points of $Γ_0(N)$, Ann. of Math. 79 (1964), 360-368.
• [11] N. Murabayashi, On normal forms of modular curves of genus 2, Osaka J. Math. 29 (1992), 405-418.
• [12] A. P. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462.
• [13] M. Yamauchi, On the traces of Hecke operators for a normalizer of $Γ_0(N)$, J. Math. Kyoto Univ. 13 (1973), 403-411.