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math.NT2023
On Matrices Arising in Finite Field Hypergeometric Functions
Satoshi Kumabe, Hasan Saad
Lehmer constructs four classes of matrices constructed from roots of unity for which the characteristic polynomials and the -th powers can be determined explicitly. Here we stud…
math.NT2022
Kampé de Fériet hypergeometric functions over finite fields
Ryojun Ito, Satoshi Kumabe, Akio Nakagawa +1
Kampé de Fériet hypergeometric functions are two-variable hypergeometric functions, which are a generalization of Appell's functions. It is known that they satisfy many reduction a…
math.NT2020
Dwork hypersurfaces of degree six and Greene's hypergeometric function
Satoshi Kumabe
In this paper, we give a formula for the number of rational points on the Dwork hypersurfaces of degree six over finite fields by using Greene's finite-field hypergeometric functio…