Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On representation of an integer as the sum of three squares and the
  ternary quadratic forms with the discriminants p^2, 16p^2   Let s(n) be the number of representations of n as the sum of three squares.
We prove a remarkable new identity for s(p^2n)- ps(n) with p being an odd
prime. This identity makes nontrivial use of ternary quadratic forms with
discriminants p^2 and 16p^2. These forms are related by Watson's
transformations. To prove this identity we employ the Siegel--Weil and the
Smith--Minkowski product formulas.

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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: funct-an