An arithmetic of modular function fields of degree two

Ryuji Sasaki

Acta Mathematica et Informatica Universitatis Ostraviensis (1999)

  • Volume: 07, Issue: 1, page 79-105
  • ISSN: 1804-1388

How to cite

top

Sasaki, Ryuji. "An arithmetic of modular function fields of degree two." Acta Mathematica et Informatica Universitatis Ostraviensis 07.1 (1999): 79-105. <http://eudml.org/doc/23829>.

@article{Sasaki1999,
author = {Sasaki, Ryuji},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {Siegel modular forms; theta functions; Kummer surfaces},
language = {eng},
number = {1},
pages = {79-105},
publisher = {University of Ostrava},
title = {An arithmetic of modular function fields of degree two},
url = {http://eudml.org/doc/23829},
volume = {07},
year = {1999},
}

TY - JOUR
AU - Sasaki, Ryuji
TI - An arithmetic of modular function fields of degree two
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 1999
PB - University of Ostrava
VL - 07
IS - 1
SP - 79
EP - 105
LA - eng
KW - Siegel modular forms; theta functions; Kummer surfaces
UR - http://eudml.org/doc/23829
ER -

References

top
  1. H. F. Baker, Abelian functions, Cambridge, 1897. Zbl0848.14012
  2. O. Bolza, Darstellung der rational ganzen Invarianten der Binarform sechsten Grades durch die Nullwerte der zugehorigen θ -Functionen, Math. Ann., 30:478-495, 1887. MR1510458
  3. A. Coble, Algebraic geometry and theta functions, Amer. Math. Soc. Coll. Publ. 10, Providence, 1929 (Reprinted 1961). (1929) MR0123958
  4. I. Dolgachev D. Ortland, Point set in projective spaces and theta funcions, Asterisque, 165, 1988. (1988) MR1007155
  5. J. Igusa, On Siegel modular forms of genus two, Amer. J. Math., 84:175-200, 1962; II, ibid. 86:392-412, 1964. (1962) MR0141643
  6. J. Igusa, On the graded rings of theta-constants, Amer. J. Math., 86:219-246, 1964, ILibid. 88:221-236, 1966. (1964) MR0164967
  7. J. Igusa, Modular forms and projective invariants, Amer. J. Math., 89:817-855, 1967. (1967) Zbl0159.50401MR0229643
  8. J. Igusa, Theta functions, Springer-Verlag, Berlin-Heiderberg-New York, 1972. (1972) Zbl0251.14016MR0325625
  9. S. Koizumi, Theta relations and projective normality of abelian varieties, Amer. J. Math., 98:865-889, 1976. (1976) Zbl0347.14023MR0480543
  10. A. Krazer, Thetafunktionen, Chelsea Pub. Co. NewYork, 1970. (1970) Zbl0212.42901
  11. L. Kronecker, Zur Theorie der elliptischen Functionen XI, Math. Werke IV, Chelsea Pub. Co. New York, 1968. (1968) 
  12. D. Mumford, On the equations defining abelian varieties I-III, , Invent. Math., 1:287-354, 1966; 3:75-135, 3:215-244, 1967. (1966) Zbl0219.14024MR0204427
  13. D. Mumford, Abelian varieties, Oxford Univ. Press, 1970. (1970) Zbl0223.14022MR0282985
  14. R. Sasaki, Modular forms vanishing at the reducible points of the Siegel upper-half space, J. reine angew. Math., 345:111-121, 1983. (1983) Zbl0513.10027MR0717889
  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. (1993) Zbl0785.14026MR1199205
  16. R. Sasaki, Moduli of curves of genus two and the special orthogonal group of degree three, (preprint, 1996). (1996) 
  17. G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press, 1971. (1971) Zbl0221.10029MR0314766
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.