Determinant formulas for multidimensional hypergeometric period matrices

AbstractIn this article we derive closed-form determinant formulas for certain period matrices whose entries are multidimensional integrals of hypergeometric type with integrands based on power functions. Our results are motivated by the work of Varchenko [Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 1206–1235; Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 146–158] and Richards and Zheng [Adv. Appl. Math. 28 (2002) 602–633] who derived closed-form expressions for determinants of matrices with entries as multidimensional integrals of rational functions