Complementaries to Kummer's degree seven reciprocity law and a Dickson Diophantine system
DOI:
https://doi.org/10.11575/cdm.v7i1.62117Abstract
Let ${\mathbb Q}(\zeta)$ be the cyclotomic field obtained from ${\mathbb Q}$ by adjoining a primitive seventh root of unity $\zeta$. Normalized primary elements of this field are characterized and related to Jacobi sums and to solutions of a system of quadratic Diophantine equations of Dickson type involving a rational prime $p\equiv 1\pmod{7}$. These objects and their connection are then used to give another formulation of the complementary laws to Kummer's reciprocity law of degree seven.Downloads
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