In two previous papers [Proc. Amer. Math. Soc.117 (1993), 877- 884], [J. Number Theory44 (1993), 214-221], a reciprocity relation for the power residue symbol of odd prime exponent, between Jacobi sums, was conjectured then proved. This is here extended to the case of an arbitrary exponent, as a consequence of an expression for the power residue character of a Jacobi sum, modulo a rational prime power, in terms of Fermat quotients.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory