Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equidistribution of Algebraic Numbers of Norm One in Quadratic Number
  Fields   Given a fixed quadratic extension K of Q, we consider the distribution of
elements in K of norm 1 (denoted N). When K is an imaginary quadratic
extension, N is naturally embedded in the unit circle in C and we show that it
is equidistributed with respect to inclusion as ordered by the absolute Weil
height. By Hilbert's Theorem 90, an element in N can be written as
\alpha/\bar{\alpha} for some \alpha \in O_K, which yields another ordering of
\mathcal N given by the minimal norm of the associated algebraic integers. When
K is imaginary we also show that N is equidistributed in the unit circle under
this norm ordering. When K is a real quadratic extension, we show that N is
equidistributed with respect to norm, under the map \beta \mapsto \log| \beta |
\bmod{\log | \epsilon^2 |} where \epsilon is a fundamental unit of O_K.

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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: chem-ph