Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Gaps between Primes in Arithmetic Progressions   For $(M,a)=1$, put \begin{equation*} G(X;M,a)=\sup_{p^\prime_n\leq
X}(p^\prime_{n+1}-p^\prime_n), \end{equation*} where $p^\prime_n$ denotes the
$n$-th prime that is congruent to $a\pmod{M}$. We show that for any positive
$C$, provided $X$ is large enough in terms of $C$, there holds
\begin{equation*} G(MX;M,a)\geq(C+o(1))\varphi(M)\frac{\log X\log_2 X\log_4 X}
{{(\log_3 X)}^2}, \end{equation*} uniformly for all $M\leq\kappa{(\log
X)}^{1/5}$ that satisfy \begin{equation*} \omega(M)\leq \exp\biggl(\frac{\log_2
M\log_4 M}{\log_3 M}\biggr). \end{equation*}

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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: math-ph