Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric theory of lower bounds on Weyl sums   We prove that the Hausdorff dimension of the set $\mathbf{x}\in [0,1)^d$,
such that $$ \left|\sum_{n=1}^N \exp\left(2 \pi i\left(x_1n+\ldots+x_d
n^d\right)\right) \right|\ge c N^{1/2} $$ holds for infinitely many natural
numbers $N$, is at least $d-1/2d$ for $d \ge 3$ and at least $3/2$ for $d=2$,
where $c$ is a constant depending only on $d$. This improves the previous lower
bound of the first and third authors for $d\ge 3$. We also obtain similar
bounds for the Hausdorff dimension of the set of large sums with monomials
$xn^d$.

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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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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: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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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: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat