Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The prime number race and zeros of Dirichlet $L$-functions off the
  critical line. III   We show, for any $q\ge 3$ and distinct reduced residues $a,b \pmod q$, the
existence of certain hypothetical sets of zeros of Dirichlet $L$-functions
lying off the critical line implies that $\pi(x;q,a)<\pi(x;q,b)$ for a set of
real $x$ of asymptotic density 1.

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The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an