Rotation Symmetries of Sequential Matrices with Applications to the Jacobi Symbol

Authors

  • Yemeen Ayub George Mason University
  • Charles L Samuels Christopher Newport University

DOI:

https://doi.org/10.46787/pump.v2i0.500

Keywords:

sequential matrices; completely multiplicative functions; quadratic reciprocity; Legendre symbol; Jacobi symbol

Abstract

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.

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Published

2019-05-24

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. https://doi.org/10.46787/pump.v2i0.500