Rotation Symmetries of Sequential Matrices with Applications to the Jacobi Symbol
Keywords: sequential matrices; completely multiplicative functions; quadratic reciprocity; Legendre symbol; Jacobi symbol
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.
How to Cite
Ayub, Y., & Samuels, C. L. (2019). Rotation Symmetries of Sequential Matrices with Applications to the Jacobi Symbol. The PUMP Journal of Undergraduate Research, 2, 87-94. Retrieved from https://journals.calstate.edu/pump/article/view/500
Copyright (c) 2019 Yemeen Ayub, Charles L Samuels
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