Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Moonshine I: Genus zero functions   We introduce a notion of Hecke-monicity for functions on certain moduli
spaces associated to torsors of finite groups over elliptic curves, and show
that it implies strong invariance properties under linear fractional
transformations. Specifically, if a weakly Hecke-monic function has algebraic
integer coefficients and a pole at infinity, then it is either a holomorphic
genus-zero function invariant under a congruence group or of a certain
degenerate type. As a special case, we prove the same conclusion for replicable
functions of finite order, which were introduced by Conway and Norton in the
context of monstrous moonshine. As an application, we introduce a class of Lie
algebras with group actions, and show that the characters derived from them are
weakly Hecke-monic. When the Lie algebras come from chiral conformal field
theory in a certain sense, then the characters form holomorphic genus-zero
functions invariant under a congruence group.

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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin