Abstract
We prove explicit formulas for certain first and second moment sums of families of Gaussian hypergeometric functions $_{n+1}F_n$, $n\ge 1$, over finite fields with $q$ elements where $q$ is an odd prime. This enables us to find an estimate for the value $_6F_5(1)$. In addition, we evaluate certain second moments of traces of the family of Clausen elliptic curves in terms of the value $_3F_2(-1)$. These formulas also allow us to express the product of certain $_2F_1$ and $_{n+1}F_n$ functions in terms of finite field Appell series which generalizes current formulas for products of $_2F_1$ functions. We finally give closed form expressions for sums of Gaussian hypergeometric functions defined using different multiplicative characters.
Citation
Ankan Pal. Bidisha Roy. Mohammad Sadek. "Moments of Gaussian hypergeometric functions over finite fields." Funct. Approx. Comment. Math. 69 (1) 77 - 92, September 2023. https://doi.org/10.7169/facm/2088
Information