Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrality of Framing and Geometric Origin of 2-functions   We say that a formal power series $\sum a_n z^n$ with rational coefficients
is a 2-function if the numerator of the fraction $a_{n/p}-p^2 a_n$ is divisible
by $p^2$ for every prime number $p$. One can prove that 2-functions with
rational coefficients appear as building block of BPS generating functions in
topological string theory. Using the Frobenius map we define 2-functions with
coefficients in algebraic number fields. We establish two results pertaining to
these functions. First, we show that the class of 2-functions is closed under
the so-called framing operation (related to compositional inverse of power
series). Second, we show that 2-functions arise naturally in geometry as
$q$-expansion of the truncated normal function associated with an algebraic
cycle extending a degenerating family of Calabi-Yau 3-folds.

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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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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: nucl-th
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The categories of this paper are: atom-ph