Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two remarks on sums of squares with rational coefficients   There exist homogeneous polynomials $f$ with $\mathbb Q$-coefficients that
are sums of squares over $\mathbb R$ but not over $\mathbb Q$. The only
systematic construction of such polynomials that is known so far uses as its
key ingredient totally imaginary number fields $K/\mathbb Q$ with specific
Galois-theoretic properties. We first show that one may relax these properties
considerably without losing the conclusion, and that this relaxation is sharp
at least in a weak sense. In the second part we discuss the open question
whether any $f$ as above necessarily has a (non-trivial) real zero. In the
minimal open cases $(3,6)$ and $(4,4)$, we prove that all examples without a
real zero are contained in a thin subset of the boundary of the sum of squares
cone.

8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
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The categories of this paper are: physics
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th