Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations by $x_1^2+2x_2^2+x_3^2+x_4^2+x_1x_3+x_1x_4+x_2x_4$   Let $r_Q(n)$ be the representation number of a nonnegative integer $n$ by the
quaternary quadratic form $Q=x_1^2+2x_2^2+x_3^2+x_4^2+x_1x_3+x_1x_4+x_2x_4$. We
first prove the identity $r_Q(p^2n)=r_Q(p^2)r_Q(n)/r_Q(1)$ for any prime $p$
different from 13 and any positive integer $n$ prime to $p$, which was
conjectured in [Eum et al, A modularity criterion for Klein forms, with an
application to modular forms of level 13, J. Math. Anal. Appl. 375 (2011),
28--41]. And, we explicitly determine a concise formula for the number
$r_Q(n^2)$ as well for any integer $n$.

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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph