Quadratic Reciprocity via Linear Algebra
نویسنده
چکیده
We adapt a method of Schur to determine the sign in the quadratic Gauss sum and derive from this, the law of quadratic reciprocity.
منابع مشابه
Quadratic Reciprocity for Root Numbers of Gl(2)
Let F be a local/global field. Let E and K be quadratic semisimple F–algebras. Let φ and λ be characters/grössencharacters of E× and K×. We define a local/global symbol ( φ λ ) to be essentially the root number of the representation BCK/F (AIE/F (φ))⊗ λ−1. In the spirit of quadratic reciprocity, we prove that ( φ λ )( λ φ ) = φ(−1)λ(−1). We then derive some consequences of this reciprocity for ...
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