On the finiteness of -adic continued fractions for number fields
arXiv preprint arXiv:2105.12570, 2021•arxiv.org
For a prime ideal $\mathfrak {P} $ of the ring of integers of a number field $ K $, we give a
general definition of $\mathfrak {P} $-adic continued fraction, which also includes classical
definitions of continued fractions in the field of $ p $--adic numbers. We give some
necessary and sufficient conditions on $ K $ ensuring that every $\alpha\in K $ admits a
finite $\mathfrak {P} $-adic continued fraction expansion for all but finitely many $\mathfrak
{P} $, addressing a similar problem posed by Rosen in the archimedean setting.
general definition of $\mathfrak {P} $-adic continued fraction, which also includes classical
definitions of continued fractions in the field of $ p $--adic numbers. We give some
necessary and sufficient conditions on $ K $ ensuring that every $\alpha\in K $ admits a
finite $\mathfrak {P} $-adic continued fraction expansion for all but finitely many $\mathfrak
{P} $, addressing a similar problem posed by Rosen in the archimedean setting.
For a prime ideal of the ring of integers of a number field , we give a general definition of -adic continued fraction, which also includes classical definitions of continued fractions in the field of --adic numbers. We give some necessary and sufficient conditions on ensuring that every admits a finite -adic continued fraction expansion for all but finitely many , addressing a similar problem posed by Rosen in the archimedean setting.
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