
D. ROY, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada 
Criteria of algebraic independence and approximation by hypersurfaces 
Given a point in , a fundamental problem is how
close one can approximate by a point of an algebraic variety
of dimension d, defined over , with degree and
logarithmic height . The problem has a different flavor
whether, for a fixed d, one wants an estimate valid for a pair
(D,T) or for infinitely many pairs (D_{n},T_{n}) chosen from a given
nondecreasing sequence of positive integers
, and a
given nondecreasing unbounded sequence of positive real numbers
with
for each . In a joint work
with Michel Laurent, we analyze the second type of problem when
d=m1. We show that, for infinitely many indices n, there exists
a
nonzero polynomial
of degree whose coefficients have absolute value
, such that Padmits at least one zero in with