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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sums of three integer squares in complex quadratic fields


Authors: Dennis R. Estes and J. S. Hsia
Journal: Proc. Amer. Math. Soc. 89 (1983), 211-214
MSC: Primary 11E12; Secondary 11R11
MathSciNet review: 712624
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Abstract: We classify all complex quadratic number fields that have all their algebraic integers expressible as a sum of three integer squares. These fields are $ F = {\mathbf{Q}}(\sqrt { - D} )$, $ D$ a positive square-free integer congruent to $ 3(\mod 8)$ and such that $ D$ does not admit a positive proper factorization $ D \equiv {d_1}{d_2}$ that satisfies simultaneously: $ {d_1} \equiv 5,7(\mod 8)$ and $ ({d_2}/{d_1}) = 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0712624-2
PII: S 0002-9939(1983)0712624-2
Keywords: Exceptional integer, genus, $ \chi $-invariant, Artin symbol
Article copyright: © Copyright 1983 American Mathematical Society