Exponential sums and finite field A-hypergeometric functions

2012/10/23 by Alan Adolphson, Adolphson, Alan
Computer Science · Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT

paper · pdf · doi:10.48550/arxiv.1210.6400

4 pages

arxiv created 2012/10/23 · openalex publication_date 2012/10/23 · arxiv updated 2012/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define finite field A-hypergeometric functions and show that they are Fourier expansions of families of exponential sums on the torus. For an appropriate choice of A, our finite field A-hypergeometric function can be specialized to the finite field _kF_k-1-hypergeometric function defined by McCarthy.

Related

• Fields of definition of finite hypergeometric functions
• Hypergeometric functions over finite fields
• Hypergeometric Functions over Finite Fields
• Product formulas for hypergeometric functions over finite fields
• Splitting Hypergeometric Functions over Roots of Unity