Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bornes effectives des fonctions d'approximation des solutions formelles
  d'\'equations binomiales   The aim of this paper is to give an effective version of the Strong Artin
Approximation Theorem for binomial equations. First we give an effective
version of the Greenberg Approximation Theorem for polynomial equations, then
using the Weierstrass Preparation Theorem, we apply this effective result to
binomial equations. We prove that the Artin function of a system of binomial
equations is bounded by a doubly exponential function in general and that it is
bounded by an affine function if the order of the approximated solutions is
bounded.

19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph