Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the distribution of $\alpha p$ modulo one in imaginary quadratic
  number fields with class number one   We investigate the distribution of $\alpha p$ modulo one in imaginary
quadratic number fields $\mathbb{K}\subset\mathbb{C}$ with class number one,
where $p$ is restricted to prime elements in the ring of integers $\mathcal{O}
= \mathbb{Z}[\omega]$ of $\mathbb{K}$. In analogy to classical work due to R.
C. Vaughan, we obtain that the inequality $\lVert\alpha p\rVert_\omega <
\mathrm{N}(p)^{-1/8+\epsilon}$ is satisfied for infinitely many $p$, where
$\lVert\varrho\rVert_\omega$ measures the distance of $\varrho\in\mathbb{C}$ to
$\mathscr{O}$ and $\mathrm{N}(p)$ denotes the norm of $p$.
  The proof is based on Harman's sieve method and employs number field
analogues of classical ideas due to Vinogradov. Moreover, we introduce a
smoothing which allows us to make conveniently use of the Poisson summation
formula.

3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph