Evaluations of hypergeometric functions over finite fields
Evans, Ron ; Greene, John
Hiroshima Math. J., Tome 39 (2009) no. 1, p. 217-235 / Harvested from Project Euclid
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We prove two general formulas for a two-parameter family of hypergeometric $\3F2(z)$ functions over a finite field $\F_q$, where $q$ is a power of an odd prime. Each formula evaluates a $\3F2$ in terms of a $\2F1$ over $\F_{q^2}$. As applications, we evaluate infinite one-parameter families of $\3F2(\frac{1}{4})$ and $\3F2(-1)$, thereby extending results of J. Greene--D. Stanton and K. Ono, who gave evaluations in special cases.
Publié le : 2009-07-15
Classification:  Hypergeometric functions over finite fields,  Gauss sums,  Jacobi sums,  Davenport--Hasse formulas,  lifted characters,  Stickelberger's congruence,  11T24,  11L05,  33C20 
@article{1249046338,
     author = {Evans, Ron and Greene, John},
     title = {Evaluations of hypergeometric functions over finite fields},
     journal = {Hiroshima Math. J.},
     volume = {39},
     number = {1},
     year = {2009},
     pages = { 217-235},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1249046338}
}

Evans, Ron; Greene, John. Evaluations of hypergeometric functions over finite fields. Hiroshima Math. J., Tome 39 (2009) no. 1, pp.  217-235. http://gdmltest.u-ga.fr/item/1249046338/