Mean values of Dirichlet polynomials and applications to linear equations with prime variables
Mean values of Dirichlet polynomials and applications to linear equations with prime variables
We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes. The latter have applications to additive problems with prime variables. In particular, we are able to improve on …