Explicit lifts of quintic Jacobi sums and period polynomials for Fq
Akinari Hoshi · Medical Entomology and Zoology · 2006
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 FP s+t by using quintic Jacobi sums for F Ps and for F pt . We also have the multiplication formula from F ps to F p ns as a special case. By the quintuplication formula, we obtain the explicit factorization of the quintic period polynomials for finite fields.