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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
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Abstract |
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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
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Mathematical Subject Classification
Primary: 11E25, 11P05
Secondary: 11R52
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Milestones
Received: 3 November 2020
Revised: 28 May 2021
Accepted: 27 June 2021
Published: 9 February 2022
Communicated by Kenneth S. Berenhaut
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Authors |
| Tim Banks | |
| Mathematics and Computer Science
Department McDaniel College Westminster, MD United States |
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| Spencer Hamblen | |
| Mathematics and Computer Science
Department McDaniel College Westminster, MD United States |
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| Tim Sherwin | |
| Mathematics and Computer Science
Department McDaniel College Westminster, MD United States |
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| Sal Wright | |
| Mathematics and Computer Science
Department McDaniel College Westminster, MD United States |
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