Quaternion Gauss Sums

Title

Quaternion Gauss Sums

Subject

Mathematics

Creator

Alexander Pilakoutas

Date

2023

Abstract

This research paper explores “quaternion Gauss sums”, which extend the quadratic Gauss sum to Hurwitz quaternions. The study investigates the properties of Quaternion Gauss sums, including their behaviour
under similarity transformations, multiplicativity, and reduced forms for diagonal matrices. Practical applications are considered, such as solution
counting in quaternion/matrix equations within prime power quotients. The research also provides a computational method for calculating quaternion Gauss sums, yielding data that informs conjectures about Gauss sum values and relates them to existing notions of matrix Gauss sums.

Files

Collection

Citation

Alexander Pilakoutas, “Quaternion Gauss Sums,” URSS SHOWCASE, accessed December 26, 2024, https://urss.warwick.ac.uk/items/show/330.