Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the S-Euclidean minimum of an ideal class   We show that the S-Euclidean minimum of an ideal class is a rational number,
generalizing a result of Cerri. We also give some corollaries which explain the
relationship of our results with Lenstra's notion of a norm-Euclidean ideal
class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. The
proof is self-contained but uses ideas from ergodic theory and topological
dynamics, particularly those of Berend.

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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess