In the second one ( 1832 ) he stated the biquadratic reciprocity law for the Gaussian integers and proved the supplementary formulas.
22.
Indeed, it was in the process of generalization of this theorem that Goro Shimura introduced his varieties and proved his reciprocity law.
23.
Hilbert's reciprocity law follows from the Artin reciprocity law and the definition of the Hilbert symbol in terms of the Artin symbol.
24.
Hilbert's reciprocity law follows from the Artin reciprocity law and the definition of the Hilbert symbol in terms of the Artin symbol.
25.
The latter property is called the " global reciprocity law " and is a far reaching generalization of the Gauss quadratic reciprocity law.
26.
The latter property is called the " global reciprocity law " and is a far reaching generalization of the Gauss quadratic reciprocity law.
27.
In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Legendre symbol is named after him.
28.
The following facts, even the reciprocity laws, are straightforward deductions from the definition of the Jacobi symbol and the corresponding properties of the Legendre symbol.
29.
A " power reciprocity law " may be formulated as an analogue of the law of quadratic reciprocity in terms of the Hilbert symbols as
30.
There are also several explicit reciprocity laws for various generalizations of the Hilbert symbol to higher local fields, " p "-divisible groups, and so on.
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