Complex multiplication formulae for hyperelliptic curves of genus three

Tokyo Journal of Mathematics

Volumn 21, Issue 2, 1998, Pages 381-431

  ŌNishi, Yoshihiro ^a  

^a IWATE UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001341733     PISSN: 03873870     EISSN: None     Source Type: Journal    
DOI: 10.3836/tjm/1270041822     Document Type: Article

References (20)

1. E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris, Geometry of Algebraic Curves, Vol. 1, Grundlehren Math. Wiss. 267 (1984), Springer.
2. H. F. Baker, Abelian Functions—Abel’s theorem and the allied theory including the theory of the theta functions—, Cambridge Univ. Press (1897, reprint 1995).
3. H. F. Baker, On the hyperelliptic sigma functions, Amer. J. Math. 20 (1898), 301-384.
4. H. F. Baker, On a system of differential equations leading to periodic functions, Acta Math. 27 (1903), 135-156.
5. E. Date and S. Tanaka, KdV Equations (in Japanese), Kinokuniya (1979).
6. G. Eisenstein, Beiträge zur Theorie der elliptischen Functionen I; II; III, Mathematische Werke Bd. II, Chelsea (1975), 299-324.
7. D. Grant, On a generalization of Jacobi’s derivative formula to dimension two, J. Reine Angew. Math. 392 (1988), 125-136.
8. D. Grant, Formal groups in genus two, J. Reine Angew. Math. 411 (1990), 96-121.
9. D. Grant, A generalization of a formula of Eisenstein, Proc. London Math. Soc. 62 (1991), 121-132.
10. S. Lang, An Introduction to Algebraic and Abelian Functions, 2nd ed., Springer (1982).
11. S. Lang, Complex Multiplication, Springer (1983).
12. C. R. Matthews, Gauss sums and elliptic functions: I. The Kummer sum, Invent. Math. 52 (1979), 163-185.
13. H.R. Matthews, Gauss sums and elliptic functions: II. The Quartic sum, Invent. Math. 54 (1979), 23-52.
14. J. S. Milne, Jacobian varieties, Arithmetic Geometry (eds. G. Cornell and J. H. Silverman), Springer (1986), 167-212.
15. D. Mumford, Tata Lectures on Theta II, Progress in Math. 43 (1984), Birkhauser.
16. D. Mumford, Abelian Varieties, Oxford Univ. Press (1985).
17. Y. Ônishi, On the Galois group corresponding to the formula of Grant, Comment. Math. Univ. St. Paul. 42 (1991), 37-48.
18. G. Shimura and Y. Taniyama, Complex Multiplication of Abelian Varieties and Its Applications to Number Theory, Publ. Math. Soc. Japan 6 (1961), Iwanami/Princeton Univ. Press.
19. T. Takenouchi, Theory of Elliptic Functions (in Japanese), Iwanami (1936).
20. G. Weber, Lehrbuch der Algebra III, Vieweg (1908); Chelsea (1961).