Using methods inherited from algebraic geometry, we give bounds for ex
ponential sums of the type Sigma(p less than or equal to x)(2 pi f(p)/
q), where q is a large prime number. f(X) is a general rational functi
on over Z and the sum is performed over primes less than x(less than o
r equal to q). Some extensions of the method are given when f(X) is of
the form f(X) = X-k + uX (k integer different from 0 and 1). (C) Else
vier, Paris.