The cubic reciprocity law can be studied in the same way as quartic reciprocity; both laws live in imaginary quadratic number fields with a finite number of units. We will proceed exactly as in the quartic case: first we study connections with the splitting of primes in certain cubic cyclic extensions, and then we use cubic Gauss and Jacobi sums to derive the cubic reciprocity law (expressed less euphemistically: this chapter won’t contain any new ideas — we just compute).
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- Cubic Reciprocity
- Springer Berlin Heidelberg