Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Additive Decompositions of Subgroups of Finite Fields   We say that a set $S$ is additively decomposed into two sets $A$ and $B$, if
$S = \{a+b : a\in A, \ b \in B\}$. Here we study additively decompositions of
multiplicative subgroups of finite fields. In particular, we give some
improvements and generalisations of results of C. Dartyge and A. Sarkozy on
additive decompositions of quadratic residues and primitive roots modulo $p$.
We use some new tools such the Karatsuba bound of double character sums and
some results from additive combinatorics.

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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys