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Sums of squares
in quaternion rings
Anna Cooke, Spencer Hamblen and Sam Whitfield
Vol. 10 (2017), No. 4, 651–664
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Abstract |
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Lagrange’s four squares theorem states that any positive integer can be expressed as the sum of four integer squares. We investigate the analogous question for quaternion rings, focusing on squares of elements of quaternion rings with integer coefficients. We determine the minimum necessary number of squares for infinitely many quaternion rings, and give global upper and lower bounds. |
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Keywords
Waring's problem, quaternions, sums of squares
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Mathematical Subject Classification 2010
Primary: 11E25, 11P05
Secondary: 11E20
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Milestones
Received: 14 November 2015
Revised: 17 April 2016
Accepted: 2 May 2016
Published: 7 March 2017
Communicated by Michael E. Zieve
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Authors |
| Anna Cooke | |
| McDaniel College 2 College Hill Westminster, MD 21157 United States |
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| Spencer Hamblen | |
| McDaniel College 2 College Hill Westminster, MD 21157 United States |
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| Sam Whitfield | |
| McDaniel College 2 College Hill Westminster, MD 21157 United States |
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