Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Fourier restriction via efficient congruencing: basic
  principles   We show that whenever $s>k(k+1)$, then for any complex sequence $(\mathfrak
a_n)_{n\in \mathbb Z}$, one has $$\int_{[0,1)^k}\left| \sum_{|n|\le N}\mathfrak
a_ne(\alpha_1n+\ldots +\alpha_kn^k) \right|^{2s}\,{\rm d}{\mathbf \alpha}\ll
N^{s-k(k+1)/2}\biggl( \sum_{|n|\le N}|\mathfrak a_n|^2\biggr)^s.$$ Bounds for
the constant in the associated periodic Strichartz inequality from $L^{2s}$ to
$l^2$ of the conjectured order of magnitude follow, and likewise for the
constant in the discrete Fourier restriction problem from $l^2$ to $L^{s'}$,
where $s'=2s/(2s-1)$. These bounds are obtained by generalising the efficient
congruencing method from Vinogradov's mean value theorem to the present
setting, introducing tools of wider application into the subject.

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The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph