This paper generalises the proof of quadratic reciprocity law in ????q[T] presented by Chun-Gang Ji and Yan Xue [2] to the case of d-th power residues, where d divides the order of ????*q. Using only elementary properties of finite fields and basic number-theoretic tools we show that if P,Q∈????q[T] are distinct irreducible polynomials then
(P/Q)d = (-1)q-1/ddeg(P)deg(Q)(Q/P)d,
where (P/Q)d is the d-th power residue symbol.
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Vol. 25 (2011)
Published: 2011-09-30
10.1515/amsil
English