| Title:
|
An arithmetic of modular function fields of degree two (English) |
| Author:
|
Sasaki, Ryuji |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
7 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
79-105 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11F46 |
| MSC:
|
11G18 |
| MSC:
|
14G35 |
| MSC:
|
14K25 |
| idZBL:
|
Zbl 1024.11031 |
| idMR:
|
MR1724136 |
| . |
| Date available:
|
2009-01-30T09:07:31Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120550 |
| . |
| Reference:
|
[1] H. F. Baker: Abelian functions.Cambridge, 1897. Zbl 0848.14012 |
| Reference:
|
[2] O. Bolza: Darstellung der rational ganzen Invarianten der Binarform sechsten Grades durch die Nullwerte der zugehorigen $\theta$-Functionen.Math. Ann., 30:478-495, 1887. MR 1510458 |
| Reference:
|
[3] A. Coble: Algebraic geometry and theta functions.Amer. Math. Soc. Coll. Publ. 10, Providence, 1929 (Reprinted 1961). MR 0123958 |
| Reference:
|
[4] I. Dolgachev D. Ortland: Point set in projective spaces and theta funcions.Asterisque, 165, 1988. MR 1007155 |
| Reference:
|
[5] J. Igusa: On Siegel modular forms of genus two.Amer. J. Math., 84:175-200, 1962; II, ibid. 86:392-412, 1964. MR 0141643 |
| Reference:
|
[6] J. Igusa: On the graded rings of theta-constants.Amer. J. Math., 86:219-246, 1964, ILibid. 88:221-236, 1966. MR 0164967 |
| Reference:
|
[7] J. Igusa: Modular forms and projective invariants.Amer. J. Math., 89:817-855, 1967. Zbl 0159.50401, MR 0229643 |
| Reference:
|
[8] J. Igusa: Theta functions.Springer-Verlag, Berlin-Heiderberg-New York, 1972. Zbl 0251.14016, MR 0325625 |
| Reference:
|
[9] S. Koizumi: Theta relations and projective normality of abelian varieties.Amer. J. Math., 98:865-889, 1976. Zbl 0347.14023, MR 0480543 |
| Reference:
|
[10] A. Krazer: Thetafunktionen.Chelsea Pub. Co. NewYork, 1970. Zbl 0212.42901 |
| Reference:
|
[11] L. Kronecker: Zur Theorie der elliptischen Functionen XI.Math. Werke IV, Chelsea Pub. Co. New York, 1968. |
| Reference:
|
[12] D. Mumford: On the equations defining abelian varieties I-III., Invent. Math., 1:287-354, 1966; 3:75-135, 3:215-244, 1967. Zbl 0219.14024, MR 0204427 |
| Reference:
|
[13] D. Mumford: Abelian varieties.Oxford Univ. Press, 1970. Zbl 0223.14022, MR 0282985 |
| Reference:
|
[14] R. Sasaki: Modular forms vanishing at the reducible points of the Siegel upper-half space.J. reine angew. Math., 345:111-121, 1983. Zbl 0513.10027, MR 0717889 |
| Reference:
|
[15] R. Sasaki: Some remarks on the moduli space of principally polarized abelian varieties with level (2,4) structure.Comp. Math. 85:87-97, 1993. Zbl 0785.14026, MR 1199205 |
| Reference:
|
[16] R. Sasaki: Moduli of curves of genus two and the special orthogonal group of degree three.(preprint, 1996). |
| Reference:
|
[17] G. Shimura: Introduction to the arithmetic theory of automorphic functions.Princeton Univ. Press, 1971. Zbl 0221.10029, MR 0314766 |
| Reference:
|
[18] H. Weber: Anwendung der Thetafunctionen zweier Veranderlicher auf die Theorie der Bewegung eines festen Korpers in einer Flüssigkeit.Math. Annalen., 14:173-206, 1879. |
| . |
