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March 2006 Explicit lifts of quintic Jacobi sums and period polynomials for $\mathbf {F}_{ {q}}$
Akinari Hoshi
Proc. Japan Acad. Ser. A Math. Sci. 82(7): 87-92 (March 2006). DOI: 10.3792/pjaa.82.87

Abstract

In this paper, we construct explicit lifts of quintic Jacobi sums for finite fields via integer solutions of Dickson's system. Namely we give a procedure to compute quintic Jacobi sums for extended field $\mathbf{F}_{p^{s+t}}$ by using quintic Jacobi sums for $\mathbf{F}_{p^s}$ and for $\mathbf{F}_{p^t}$. We also have the multiplication formula from $\mathbf{F}_{p^s}$ to $\mathbf{F}_{p^{ns}}$ as a special case. By the quintuplication formula, we obtain the explicit factorization of the quintic period polynomials for finite fields.

Citation

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Akinari Hoshi. "Explicit lifts of quintic Jacobi sums and period polynomials for $\mathbf {F}_{ {q}}$." Proc. Japan Acad. Ser. A Math. Sci. 82 (7) 87 - 92, March 2006. https://doi.org/10.3792/pjaa.82.87

Information

Published: March 2006
First available in Project Euclid: 10 October 2006

zbMATH: 1116.11093
MathSciNet: MR2265605
Digital Object Identifier: 10.3792/pjaa.82.87

Subjects:
Primary: 11E25, 11L05, 11T22, 11T24

Rights: Copyright © 2006 The Japan Academy

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Vol.82 • No. 7 • March 2006
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