Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identities Involving Zeros of Ramanujan and Shanks Cubic Polynomials   In this paper we highlight the connection between Ramanujan cubic polynomials
(RCPs) and a class of polynomials, the Shanks cubic polynomials (SCPs), which
generate cyclic cubic fields. In this way we provide a new characterization for
RCPs and we express the zeros of any RCP in explicit form, using trigonometric
functions. Moreover, we observe that a cyclic transform of period three
permutes these zeros. As a consequence of these results we provide many new and
beautiful identities. Finally we connect RCPs to Gaussian periods, finding a
new identity, and we study some integer sequences related to SCPs .

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph