Sums of three integer squares in complex quadratic fields
Sums of three integer squares in complex quadratic fields
We classify all complex quadratic number fields that have all their algebraic integers expressible as a sum of three integer squares. These fields are <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F equals bold upper Q left-parenthesis StartRoot negative upper D EndRoot right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi …