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, Série 4, Volume 16 (1989) no. 4, p. 557-578
@article{ASNSP_1989_4_16_4_557_0,
     author = {Matsumoto, Keiji},
     title = {On modular functions in 2 variables attached to a family of hyperelliptic curves of genus 3},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 16},
     number = {4},
     year = {1989},
     pages = {557-578},
     zbl = {0708.11029},
     mrnumber = {1052734},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1989_4_16_4_557_0}
}
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, Série 4, Volume 16 (1989) no. 4, pp. 557-578. http://www.numdam.org/item/ASNSP_1989_4_16_4_557_0/

[1] P. Deligne - G.D. Mostow, Monodromy of hypergeometric functions and non-lattice integral monodromy, Publ. Math I.H.E.S., 63 (1986), pp. 5-88. | Numdam | MR 849651 | Zbl 0615.22008

[2] T. Kimura, Hypergeometric Functions of Two Variables, Lecture Notes, Tokyo Univ., (1973).

[3] R.P. Holzapfel, Zweidimensionale periodische Funktionentheorie der Kugel, Akademie der Wissenschaften der DDR, Berlin, (1983).

[4] D. Mumford, Tata Lectures on Theta I-II, Birkhauser, Boston-Basel-Stuttgard, (1983). | MR 688651 | Zbl 0509.14049

[5] E. Picard, Sur les fonctions de deux variables independentes analogues aux fonctions modulaires, Acta Math., 2 (1883), pp. 114-135. | JFM 15.0432.01

[6] I.I. Pjateckii-Sapiro, Geometry of Classical Domains and Automorphic Functions, Fizmatgiz, Moscow, (1961).

[7] H.E. Rauch - H.M. Farkas, Theta Functions with Applications to Reimann Surfaces, Williams and Wilkins, Baltimore, (1974). | MR 352108 | Zbl 0292.30015

[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. | MR 512815 | Zbl 0371.32024

[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. | Numdam | Numdam | MR 563337 | Zbl 0501.14019

[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). | MR 966178 | Zbl 0678.10020

[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. | MR 481156 | Zbl 0279.32022

[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. | Zbl 0506.33001

[13] M. Yoshida, Fuchsian Differential Equations, Vieweg, Verlag, Wiesbaden, (1987). | MR 986252 | Zbl 0618.35001

[14] I. Wakabayashi, Note on Picard's modular function of two variables, private note.