ON SOME EXPONENTIAL-SUMS OVER PRIME-NUMBE RS

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.