An analogue of the nearest integer continued fraction for certain cubic irrationalities
An analogue of the nearest integer continued fraction for certain cubic irrationalities
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="theta"> <mml:semantics> <mml:mi>θ<!-- θ --></mml:mi> <mml:annotation encoding="application/x-tex">\theta</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be any irrational and define <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N e left-parenthesis theta right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>e</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>θ<!-- θ --></mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">Ne(\theta )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to be …