On 𝑈_{𝑚}-numbers

Abstract

In this paper we shall give some examples of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U Subscript m"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{U_m}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-numbers by using the continued fraction expansions of algebraic numbers of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m greater-than 1"> <mml:semantics> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">m &gt; 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

Locations

• Proceedings of the American Mathematical Society - View - PDF