Sums of three integer squares in complex quadratic fields
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- by Dennis R. Estes and J. S. Hsia PDF
- Proc. Amer. Math. Soc. 89 (1983), 211-214 Request permission
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 $({d_2}/{d_1}) = 1$.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 211-214
- MSC: Primary 11E12; Secondary 11R11
- DOI: https://doi.org/10.1090/S0002-9939-1983-0712624-2
- MathSciNet review: 712624