Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exceptional characters and nonvanishing of Dirichlet $L$-functions   Let $\psi$ be a real primitive character modulo $D$. If the $L$-function
$L(s,\psi)$ has a real zero close to $s=1$, known as a Landau-Siegel zero, then
we say the character $\psi$ is exceptional. Under the hypothesis that such
exceptional characters exist, we prove that at least fifty percent of the
central values $L(1/2,\chi)$ of the Dirichlet $L$-functions $L(s,\chi)$ are
nonzero, where $\chi$ ranges over primitive characters modulo $q$ and $q$ is a
large prime of size $D^{O(1)}$. Under the same hypothesis we also show that,
for almost all $\chi$, the function $L(s,\chi)$ has at most a simple zero at $s
= 1/2$.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat