Vol. 14, No. 5, 2021

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Sums of quaternion squares and a theorem of Watson

Tim Banks, Spencer Hamblen, Tim Sherwin and Sal Wright

Vol. 14 (2021), No. 5, 783–792
Abstract

We use a representability theorem of G. L. Watson to examine sums of squares in quaternion rings with integer coefficients. This allows us to determine a large family of such rings where every element expressible as the sum of squares can be written as the sum of three squares.

Keywords
Waring's problem, quaternions, Hilbert–Waring theorem
Mathematical Subject Classification
Primary: 11E25, 11P05
Secondary: 11R52
Milestones
Received: 3 November 2020
Revised: 28 May 2021
Accepted: 27 June 2021
Published: 9 February 2022

Communicated by Kenneth S. Berenhaut
Authors
Tim Banks
Mathematics and Computer Science Department
McDaniel College
Westminster, MD
United States
Spencer Hamblen
Mathematics and Computer Science Department
McDaniel College
Westminster, MD
United States
Tim Sherwin
Mathematics and Computer Science Department
McDaniel College
Westminster, MD
United States
Sal Wright
Mathematics and Computer Science Department
McDaniel College
Westminster, MD
United States