Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertical shift and simultaneous Diophantine approximation on polynomial
  curves   The Hausdorff dimension of the set of simultaneously tau well approximable
points lying on a curve defined by a polynomial P(X)+alpha, where P(X) is a
polynomial with integer coefficients and alpha is in R, is studied when tau is
larger than the degree of P(X). This provides the first results related to the
computation of the Hausdorff dimension of the set of well approximable points
lying on a curve which is not defined by a polynomial with integer
coefficients. The proofs of the results also include the study of problems in
Diophantine approximation in the case where the numerators and the denominators
of the rational approximations are related by some congruential constraint.

13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th