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.
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 May 16, 2024, https://urss.warwick.ac.uk/items/show/354.