In this paper, we give a Thomae type formula for K3 surfaces X given by double covers of the projective plane branching along six lines. This formula gives relations between theta constants on the bounded symmetric domain of type I22 and period integrals of X. Moreover, we express the period integrals by using the hypergeometric function FS of four variables. As applications of our main theorem, we define ℝ4-valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function FS.
© by Walter de Gruyter Berlin Boston