Confluence of cycles for hypergeometric functions on 𝑍_{2,𝑛+1}

Abstract

The hypergeometric function of general type, which is a generalization of the classical confluent hypergeometric functions, admits an integral representation derived from a character of a linear abelian group. For the hypergeometric function on the space of 2 × ( n + 1 ) 2\times (n+1) matrices, a basis of cycles for the integral is constructed by a limit process, which is called a process of confluence. The determinant of the period matrix is explicitly evaluated to show the independence of the cycles.