Kummer, Eisenstein, Computing Gauss Sums as Lagrange Resolvents
نویسنده
چکیده
In fact, [Eisenstein 1850] evaluated cubes and fourth powers of Gauss sums attached to cubic and quartic characters to prove the corresponding reciprocity laws. One essential point is the p-adic approximation of Gauss sums by [Kummer 1847], generalized in [Stickelberger 1890]. Since the rings of algebraic integers generated by third or fourth roots of unity have class number one and finitely-many units, cubic (and sextic) and quartic subfields of cyclotomic fields are readily expressible in radicals, via Lagrange resolvents.
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تاریخ انتشار 2010