We derive an explicit formula for Hecke Gauss sums of quadratic number fields. As an immediate consequence we obtain a quadratic reciprocity law in quadratic number fields which generalizes the classical one given by Hecke. The proofs use, apart from the well-known formulas for ordinary Gauss sums, only elementary algebraic manipulations.
We derive an explicit formula for Hecke-Gauss sums of quadratic
number fi elds. As an immediate consequence we obtain a quadratic reciprocity
law in quadratic number fi elds which generalizes the classical one given by
Hecke. The proofs use, apart from the well-known formulas for ordinary Gauss
sums, only elementary algebraic manipulations.
