Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-classical polynomials and the inverse theorem   In this note we characterize when non-classical polynomials are necessary in
the inverse theorem for the Gowers $U^k$-norm. We give a brief deduction of the
fact that a bounded function on $\mathbb F_p^n$ with large $U^k$-norm must
correlate with a classical polynomial when $k\leq p+1$. To the best of our
knowledge, this result is new for $k=p+1$ (when $p>2$). We then prove that
non-classical polynomials are necessary in the inverse theorem for the Gowers
$U^k$-norm over $\mathbb F_p^n$ for all $k\geq p+2$, completely characterizing
when classical polynomials suffice.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: chem-ph