Modular equations of hyperelliptic X₀(N) and an application

• Autorzy: Takeshi Hibino , Naoki Murabayashi
• Języki publikacji: EN

Kategorie tematyczne

• 14H45: Special curves and curves of low genus
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 14G05: Rational points
• 11G05: Elliptic curves over global fields
• 11F11: Holomorphic modular forms of integral weight

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 3
• Strony: 279-291

Daty

wydano

1997

otrzymano

1996-10-09

poprawiono

1997-03-26

Twórcy

autor

Takeshi Hibino

• Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, Japan

autor

Naoki Murabayashi

• Department of Mathematical Sciences and Faculty of Science, Yamagata University, 1-4-12, Koshirakawa-cho, Yamagata-shi, Yamagata 990, Japan

Bibliografia

• [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160.
• [2] N. D. Elkies, Explicit isogenies, preprint.
• [3] R. Fricke, Die Elliptischen Funktionen und ihre Anwendungen, Teubner, Leipzig, 1922.
• [4] K. Hashimoto, On Brandt matrices of Eichler orders, preprint.
• [5] H. Hijikata, Explicit formula of the traces of Hecke operators for Γ₀(N), J. Math. Soc. Japan 26 (1974), 56-82.
• [6] M. A. Kenku and F. Momose, Automorphism groups of the modular curve X₀(N), Compositio Math. 65 (1988), 51-80.
• [7] B. Mazur, Rational points on modular curves, in: Modular Functions of One Variable V (Bonn, 1976), Lecture Notes in Math. 601, Springer, Berlin, 1977, 107-148.
• [8] F. Momose, Rational points on the modular curves $X_split(p)$, Compositio Math. 52 (1984), 115-137.
• [9] N. Murabayashi, On normal forms of modular curves of genus 2, Osaka J. Math. 29 (1992), 405-418.
• [10] A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462.
• [11] A. Pizer, An algorithm for computing modular forms on Γ₀(N), J. Algebra 64 (1980), 340-390.
• [12] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton Univ. Press, 1971.
• [13] M. Shimura, Defining equations of modular curves X₀(N), Tokyo J. Math. 18 (1995), 443-456.
• [14] M. Yamauchi, On the traces of Hecke operators for a normalizer of Γ₀(N), J. Math. Kyoto Univ. 13 (1973), 403-411.