Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates on the number of rational solutions of variants of diagonal
  equations over finite fields   In this paper we study the set of rational solutions of equations defined by
power sums symmetric polynomials with coefficients in a finite field. We do
this by means of applying a methodology which relies on the study of the
geometry of the set of common zeros of symmetric polynomials over the algebraic
closure of a finite field. We provide improved estimates and existence results
of rational solutions to the following equations: deformed diagonal equations,
generalized Markoff Hurwitz type equations and Carlitz's equations. We extend
these techniques to a more general variants of diagonal equations over finite
fields.

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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys