On polynomial reciprocity law.
The quadratic reciprocity law was generalized to polynomials by Carlitz. Here we have another proof deduced from an appropriate generalization to polynomials of Jacobi symbols, namely the author considers essentially \[ \text{Jacobi}(a,m) = \text{Resultant}(n,a). \] Where \(n\) is the unique monic polynomial scalar multiple of \(m.\) A polynomial version of the biquadratic law of reciprocity is also obtained. Moreover, by using analytic methods, the author is able to generalize appropriately also the value of quadratic Gauss sums.
scientific article; zbMATH DE number 1957099