On modular functions in 2 variables attached to a family of hyperelliptic curves of genus 3

Keiji Matsumoto

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)

  • Volume: 16, Issue: 4, page 557-578
  • ISSN: 0391-173X

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Matsumoto, Keiji. "On modular functions in 2 variables attached to a family of hyperelliptic curves of genus 3." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.4 (1989): 557-578. <http://eudml.org/doc/84062>.

@article{Matsumoto1989,
author = {Matsumoto, Keiji},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {hyperelliptic curves; Siegel upper half-space; monodromy group},
language = {eng},
number = {4},
pages = {557-578},
publisher = {Scuola normale superiore},
title = {On modular functions in 2 variables attached to a family of hyperelliptic curves of genus 3},
url = {http://eudml.org/doc/84062},
volume = {16},
year = {1989},
}

TY - JOUR
AU - Matsumoto, Keiji
TI - On modular functions in 2 variables attached to a family of hyperelliptic curves of genus 3
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1989
PB - Scuola normale superiore
VL - 16
IS - 4
SP - 557
EP - 578
LA - eng
KW - hyperelliptic curves; Siegel upper half-space; monodromy group
UR - http://eudml.org/doc/84062
ER -

References

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  2. [2] T. Kimura, Hypergeometric Functions of Two Variables, Lecture Notes, Tokyo Univ., (1973). 
  3. [3] R.P. Holzapfel, Zweidimensionale periodische Funktionentheorie der Kugel, Akademie der Wissenschaften der DDR, Berlin, (1983). 
  4. [4] D. Mumford, Tata Lectures on Theta I-II, Birkhauser, Boston-Basel-Stuttgard, (1983). Zbl0509.14049MR688651
  5. [5] E. Picard, Sur les fonctions de deux variables independentes analogues aux fonctions modulaires, Acta Math., 2 (1883), pp. 114-135. JFM15.0432.01
  6. [6] I.I. Pjateckii-Sapiro, Geometry of Classical Domains and Automorphic Functions, Fizmatgiz, Moscow, (1961). 
  7. [7] H.E. Rauch - H.M. Farkas, Theta Functions with Applications to Reimann Surfaces, Williams and Wilkins, Baltimore, (1974). Zbl0292.30015MR352108
  8. [8] H.L. Resnikoff - Y.S. Tai, On the structure of a graded ring of automorphic forms on the 2-dimensional complex ball, Math. Ann.238 (1978), pp. 97-117. Zbl0371.32024MR512815
  9. [9] H. Shiga, One attempt to the K3 modular function I-II, Ann. Scuola Norm. Pisa, Serie IV-VI(1979), pp. 609-635, Serie IV-VIII(1981), pp. 157-182. Zbl0501.14019MR563337
  10. [10] H. Shiga, On the representation of the Picard modular function by theta constants I-II, to appear in Pub. R.I.M.S. Kyoto Univ., 24 (1988). Zbl0678.10020MR966178
  11. [11] T. Terada, Problème de Riemann et fonctions automorphes provenant des fonctions hypergeometriques de plusieurs variables, J. Math. Kyoto Univ., 13 (1973), pp. 557-578. Zbl0279.32022MR481156
  12. [12] T. Terada, Fonctions Hypergeometriques F1 et fonctions automorphes I-II, J. Math. Soc. Japan, 35 (1983), pp. 451-475, 37 (1985), pp. 173-185. Zbl0506.33001
  13. [13] M. Yoshida, Fuchsian Differential Equations, Vieweg, Verlag, Wiesbaden, (1987). Zbl0618.35001MR986252
  14. [14] I. Wakabayashi, Note on Picard's modular function of two variables, private note. 

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