Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L-functions for Meromorphic Modular Forms and Sum Rules in Conformal
  Field Theory   We define L-functions for meromorphic modular forms that are regular at
cusps, and use them to: (i) find new relationships between Hurwitz class
numbers and traces of singular moduli, (ii) establish predictions from the
physics of T-reflection, and (iii) express central charges in two-dimensional
conformal field theories (2d CFT) as a literal sum over the states in the CFTs
spectrum. When a modular form has an order-$p$ pole away from cusps, its
$q$-series coefficients grow as $n^{p-1} e^{2 \pi n t}$ for $t \geq
\sqrt{3}/2$. Its L-function must be regularized. We define such L-functions by
a deformed Mellin transform. We study the L-functions of logarithmic
derivatives of modular forms.L-functions of logarithmic derivatives of
Borcherds products reveal a new relationship between Hurwitz class numbers and
traces of singular moduli. If we can write 2d CFT path integrals as infinite
products, our L-functions confirm T-reflection predictions and relate central
charges to regularized sums over the states in a CFTs spectrum. Equating
central charges, which are a proxy for the number of degrees of freedom in a
theory, directly to a sum over states in these CFTs is new and relies on our
regularization of such sums that generally exhibit exponential (Hagedorn)
divergences.

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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
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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: 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-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: physics