Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hecke System of Harmonic Maass Functions and Applications to Modular
  Curves of Higher Genera   In Monstrous moonshine, genus 0 property and the notion of replicability are
strongly connected. With regards to recent developments of moonshine, we
investigate a higher genus generalization of replicability for a general
automorphic form. Specifically, we extend the definitions of replicates and a
Hecke operator to harmonic Maass functions on modular curves of higher genera
to obtain number theoretic generalizations of important results in Monstrous
moonshine. Furthermore, we show the utility of the extended notions in yielding
uniform proofs for numerous arithmetic properties of Fourier coefficients of
modular functions of arbitrary level, which have been proved only for special
cases of curves of genus zero or small prime levels.

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio