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2017 Sums of squares in quaternion rings
Anna Cooke, Spencer Hamblen, Sam Whitfield
Involve 10(4): 651-664 (2017). DOI: 10.2140/involve.2017.10.651

Abstract

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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Anna Cooke. Spencer Hamblen. Sam Whitfield. "Sums of squares in quaternion rings." Involve 10 (4) 651 - 664, 2017. https://doi.org/10.2140/involve.2017.10.651

Information

Received: 14 November 2015; Revised: 17 April 2016; Accepted: 2 May 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06699711
MathSciNet: MR3630308
Digital Object Identifier: 10.2140/involve.2017.10.651

Subjects:
Primary: 11E25, 11P05
Secondary: 11E20

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2017
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