Totally positive units and squares
Totally positive units and squares
Let<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"><mml:semantics><mml:mi>K</mml:mi><mml:annotation encoding="application/x-tex">K</mml:annotation></mml:semantics></mml:math></inline-formula>be a finite cyclic extension of the rational number field<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q"><mml:semantics><mml:mi>Q</mml:mi><mml:annotation encoding="application/x-tex">Q</mml:annotation></mml:semantics></mml:math></inline-formula>, with Galois group<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G left-parenthesis upper K slash upper Q right-parenthesis"><mml:semantics><mml:mrow><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>K</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>/</mml:mo></mml:mrow><mml:mi>Q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">G(K/Q)</mml:annotation></mml:semantics></mml:math></inline-formula>of order<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Superscript a"><mml:semantics><mml:mrow class="MJX-TeXAtom-ORD"><mml:msup><mml:mi>p</mml:mi><mml:mi>a</mml:mi></mml:msup></mml:mrow><mml:annotation encoding="application/x-tex">{p^a}</mml:annotation></mml:semantics></mml:math></inline-formula>for an odd prime<inline-formula content-type="math/mathml"><mml:math …