Rational points on certain abelian varieties over function fields (Q1345281)

This is a continuation of previous papers by the author [J. Number Theory 37, No. 2, 168-172 (1991; Zbl 0729.14019) and Tôhoku Math. J., II. Ser. 44, No. 3, 335-344 (1992; Zbl 0759.14034)]. The author constructs explicitly a three parameter family of elliptic curves defined over the field of rational numbers with generic Mordell-Weil rank four. The construction is based on a generalization of the Prym varieties, which deals with double covers of varieties of arbitrary dimension.