Mean values of Dirichlet polynomials and applications to linear equations with prime variables

Details 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

2004-12-12

arxiv.org/abs/math/0412227v1

Acta Arith. 123 (2006), 125-142

Mathematics

Number Theory

Scientific paper

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 a recent result of J.Y. Liu and K.M. Tsang on the size of the solutions of linear equations with prime variables.

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