Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving effectively some families of Thue Diophantine equations   Let $\alpha$ be an algebraic number of degree $d\ge 3$ and let $K$ be the
algebraic number field $\Q(\alpha)$. When $\varepsilon$ is a unit of $K$ such
that $\Q(\alpha\varepsilon)=K$, we consider the irreducible polynomial
$f_\varepsilon(X) \in \Z[X]$ such that $f_\varepsilon(\alpha\varepsilon)=0$.
Let $F_\varepsilon(X,Y)$ be the irrreducible binary form of degree $d$
associated to $f_{\varepsilon}(X) $ under the condition
$F_{\varepsilon}(X,1)=f_{\varepsilon}(X)$. For each positive integer $m$, we
want to exhibit an effective upper bound for the solutions $(x,y,\varepsilon)$
of the diophantine inequation $|F_\varepsilon(x,y)|\le m$. We achieve this goal
by restricting ourselves to a subset of units $\varepsilon$ which we prove to
be sufficiently large as soon as the degree of $K$ is $\geq 4$.

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th