Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of a conjecture of Farkas and Kra   In this paper we prove a conjectured modular equation of Farkas and Kra,
which involving a half sum of certain modular form of weight $1$ for congruence
subgroup $\Gamma_1(k)$ with any prime $k$. We prove that their conjectured
identity holds for all odd integer $k\ge 2$. A new modular equation of Farkas
and Kra type is also established.

29
The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: stat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph