On Matrices Arising in the Finite Field Analogue of Euler’s Integral Transform

Abstract

In his 1984 Ph.D. thesis, J. Greene defined an analogue of the Euler integral transform for finite field hypergeometric series. Here we consider a special family of matrices which arise naturally in the study of this transform and prove a conjecture of Ono about the decomposition of certain finite field hypergeometric functions into functions of lower dimension.

Keywords

• hypergeometric series
• finite fields
• Euler integral transform