On the Siegel modular function field of degree three

S. Tsuyumine

Compositio Mathematica (1987)

  • Volume: 63, Issue: 1, page 83-98
  • ISSN: 0010-437X

How to cite

top

Tsuyumine, S.. "On the Siegel modular function field of degree three." Compositio Mathematica 63.1 (1987): 83-98. <http://eudml.org/doc/89853>.

@article{Tsuyumine1987,
author = {Tsuyumine, S.},
journal = {Compositio Mathematica},
keywords = {Siegel modular group; Siegel modular function field; seven generators of },
language = {eng},
number = {1},
pages = {83-98},
publisher = {Martinus Nijhoff Publishers},
title = {On the Siegel modular function field of degree three},
url = {http://eudml.org/doc/89853},
volume = {63},
year = {1987},
}

TY - JOUR
AU - Tsuyumine, S.
TI - On the Siegel modular function field of degree three
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 63
IS - 1
SP - 83
EP - 98
LA - eng
KW - Siegel modular group; Siegel modular function field; seven generators of
UR - http://eudml.org/doc/89853
ER -

References

top
  1. 1 F.A. Bogomolov and P.I. Katsylo: Rationality of some quotoent varieties. Math. USSR Sbornik54 (1986) 571-576. Zbl0591.14040
  2. 2 G. Frobenius: Über die Beziehungen zwischen den 28 Doppel-tangenten einer ebenen Curve vierter Ordnung. J. Reine Angew. Math.99 (1886) 275-314. Zbl18.0696.01JFM18.0696.01
  3. 3 J. Igusa: On Siegel modular forms of genus two. Amer. J. Math.84 (1962) 175-200. Zbl0133.33301MR141643
  4. 4 J. Igusa: On Siegel modular forms of genus two (II). Amer. J. Math.86 (1964) 392-412. Zbl0133.33301MR168805
  5. 5 J. Igusa: Modular forms and projective invariants. Amer. J. Math.89 (1967) 817-855. Zbl0159.50401MR229643
  6. 6 J. Kollár and F.O. Schreyer: The moduli of curves is stably rational for g ≦ 6. Duke Math. J.51 (1984) 239-242. Zbl0576.14027
  7. 7 H. Maass: Die Fourierkoeffizienten der Eisensteinreihen zweiten Grades. Mat. Fys. Medd. Vid. Selsk.38, 14 (1964). Zbl0244.10023MR171758
  8. 8 M. Ozeki and T. Washio: Explicit formulas for the Fourier coefficients (of Eistenstein series of degree 3). J. Reine. Angew. Math.345 (1983) 148-171. Zbl0512.10022MR717891
  9. 9 M. Ozeki and T. Washio: A table of the Fourier coefficients of Eistenstein series of degree 3. Proc. Japan Acad. Ser.A59 (1983) 252-255. Zbl0522.10018MR718614
  10. 10 S. Raghavan: On Eisenstein series of degree 3. J. Indian Math. Soc. (N.S.) 39 (1975) 103-120. Zbl0412.10020MR414493
  11. 11 B. Riemann: Zur Theorie der Abel'schen Funktionen für den Fall p = 3. In: Math. Werke. Teubener, Leipzig (1876) 456-476. 
  12. 12 R. Sasaki: On the equations defining curves of genus three and the moduli (Japanese). In: Around theta functions and Siegel modular forms. RIMS Kokyuroku447 (1982) 17-31. 
  13. 13 G. Shimura: On the zeta function of an abelian variety with complex multiplication. Ann. Math. (2) 94 (1971) 504-533. Zbl0242.14009MR288089
  14. 14 G. Shimura: On the field of rationality for an abelian variety. Nagoya Math. J.45 (1972) 167-178. Zbl0243.14012MR306215
  15. 15 G. Shimura: On the real points of an arithmetic quotient of a bounded symmetric domain. Math. Ann.215 (1975) 135-164. Zbl0394.14007MR572971
  16. 16 C.L. Siegel: Einführung in die Theorie der Modulfunktionen n-ten Grades. Math. Ann.116 (1939) 617-657. Zbl0021.20302MR1251JFM65.0357.01
  17. 17 C.L. Siegel: Moduln Abelscher Funktionen. Nachr. Akad. Wiss. Gòttingen25365-427. Zbl0122.32102MR166196
  18. 18 C.L. Siegel: Topics in complex function theory, Vol. 3. Wiley-Interscience, New York, (1973). Zbl0184.11201MR476762
  19. 19 S. Tsuyumine: On Siegel modular forms of degree three. Amer. J. Math.108 (1986) 755-862;Addendum, ibid., 1001-1003. Zbl0602.10015MR853217
  20. 20 H. Weber: Theorie der Abel'schen Funktionen vom Geschlecht 3. Berlin (1876). JFM08.0293.01

NotesEmbed ?

top

You must be logged in to post comments.