Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal integral bases and Gaussian periods in the simplest cubic fields   We give all normal integral bases for the simplest cubic field $L_n$
generated by the roots of Shanks' cubic polynomial when these bases exist, that
is, $L_n/\mathbb Q$ is tamely ramified. Furthermore, as an application of the
result, we give an explicit relation between the roots of Shanks' cubic
polynomial and the Gaussian periods of $L_n$ in the case $L_n/\mathbb Q$ is
tamely ramified, which is a generalization of the work of Lehmer, Ch\^{a}telet
and Lazarus in the case that the conductor of $L_n$ is equal to $n^2+3n+9$.

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The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph