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Let $ \alpha $ be an algebraic number of degree $ d\geq 2 $ . We consider the set $ E(\alpha) $ of positive integers $ n $ such that… Click to show full abstract
Let $ \alpha $
be an algebraic number of degree $ d\geq 2 $
.
We consider the set $ E(\alpha) $
of positive integers
$ n $
such that the primitive $ n $
th root of unity $ e^{2\pi i/n} $
is expressible as a quotient of two conjugates of
$ \alpha $
over
$ {} $
.
In particular, our results imply that
$ E(\alpha) $
is small. We prove that
$ |E(\alpha)|
Keywords:
number;
algebraic number;
conjugates algebraic;
two conjugates;
cyclotomic quotients;
quotients two
Journal Title: Siberian Mathematical Journal
Year Published: 2021
Link to full text (if available)
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Journal Title: Siberian Mathematical Journal
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!