Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaps of Smallest Possible Order between Primes in an Arithmetic
  Progression   Let $t \in \mathbb{N}$, $\eta >0$. Suppose that $x$ is a sufficiently large
real number and $q$ is a natural number with $q \leq x^{5/12-\eta}$, $q$ not a
multiple of the conductor of the exceptional character $\chi^*$ (if it exists).
Suppose further that, \[ \max \{p : p | q \} < \exp (\frac{\log x}{C \log \log
x}) \; \; {and} \; \; \prod_{p | q} p < x^{\delta}, \] where $C$ and $\delta$
are suitable positive constants depending on $t$ and $\eta$. Let $a \in
\mathbb{Z}$, $(a,q)=1$ and \[ \mathcal{A} = \{n \in (x/2, x]: n \equiv a
\pmod{q} \} . \] We prove that there are primes $p_1 < p_2 < ... < p_t$ in
$\mathcal{A}$ with \[ p_t - p_1 \ll qt \exp (\frac{40 t}{9-20 \theta}) . \]
Here $\theta = (\log q) / \log x$.

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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph