Abstract:
An estimation of the modulus of an exponential sum over primes
$$
S_2(\alpha;x,1)=\sum_{n\le x}\Lambda(n) e(\alpha(n+1)^2)
$$
is obtained, where $\alpha$ is approximated by a rational number with a large denominator.
Key words:exponential sum, prime numbers, Mobius function, Mangoldt function.