Rotation Symmetries of Sequential Matrices with Applications to the Jacobi Symbol
Yemeen Ayub, Charles L. Samuels · The PUMP Journal of Undergraduate Research · 2019
Using an action of the dihedral group on sets of square matrices, we identify various symmetry properties of sequential matrices with integer entries. We then use those properties to identify new symmetries involving the Legendre and Jacobi symbols. Our work generalizes several well-known facts in quadratic reciprocity.