Quadratic Forms and Reciprocity

This group gathers theorems about quadratic residues, the law of quadratic reciprocity that relates them, and the closely related theory of quadratic forms and the integer lattices built from them. It covers Euler's criterion and Gauss's reciprocity law along with its many later proofs, the Hasse-Minkowski local-global principle for when a quadratic form represents zero, the theorems naming which numbers a given quadratic form can represent, and the exceptional lattice results behind the densest known sphere packings in eight and twenty-four dimensions.