Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for discrete moments of Weyl sums and applications   We prove two bounds for discrete moments of Weyl sums. The first one can be
obtained using a standard approach. The second one involves an observation how
this method can be improved, which leads to a sharper bound in certain ranges.
The proofs both build on the recently proved main conjecture for Vinogradov's
mean value theorem.
  We present two selected applications: First, we prove a new $k$- th
derivative test for the number of integer points close to a curve by an
exponential sum approach. This yields a stronger bound than existing results
obtained via geometric methods, but it is only applicable for specific
functions. As second application we prove a new improvement of the polynomial
large sieve inequality for one-variable polynomials of degree $k \geq 4$.

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The categories of this paper are: cond-mat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
26
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: hep-ex
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio