Abstract
We express the number of \({\mathbb{F}_q}\) -points on the hyperelliptic curve \({\alpha{y}^2=\beta{x}^f + \gamma}\) in terms of Gaussian hypergeometric series. We also find some special values of \({{_{2}}F_1}\) -Gaussian hypergeometric series containing characters of order 3 and 4 as parameters.
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Barman, R., Kalita, G. & Saikia, N. Hyperelliptic curves and values of Gaussian hypergeometric series. Arch. Math. 102, 345–355 (2014). https://doi.org/10.1007/s00013-014-0633-5
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DOI: https://doi.org/10.1007/s00013-014-0633-5