One attempt to the K3 modular function I
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 6 (1979) no. 4, p. 609-635
@article{ASNSP_1979_4_6_4_609_0,
     author = {Shiga, Hironori},
     title = {One attempt to the $K3$ modular function I},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 6},
     number = {4},
     year = {1979},
     pages = {609-635},
     zbl = {0427.14013},
     mrnumber = {563337},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1979_4_6_4_609_0}
}
Shiga, Hironori. One attempt to the $K3$ modular function I. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 6 (1979) no. 4, pp. 609-635. http://www.numdam.org/item/ASNSP_1979_4_6_4_609_0/

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

[2] P. Appell-Kampé DE FÉRIET, Fonctions Hypergéométriques et Hypersphériques. Polynomes d'Hermite, Paris, Gauthier-Villars, 1926. | JFM 52.0361.13

[3] K. Kodaira, On compact analytic surfaces, II-III, Ann. of Math., 77 (1963), pp. 563-626; 78 (1963), pp. 1-40. | MR 184257 | Zbl 0118.15802

[4] K. Kodaira, On the structure of compact complex analytic surfaces, I, Amer. J. Math., 86 (1964), pp. 751-798. | MR 187255 | Zbl 0137.17501

[5] H. Shiga, One attempt to the K3 modular function (announcement), Proceedings of International Conferences on Several Complex Variables, Cortona, 1976-77. | Zbl 0425.14007