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

Source: [Mean values of Dirichlet polynomials and applications to linear equations with prime variables](<https://www.sota2.com/research/paper/68fa520b1e209131ce977a70>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T11:40:11.924Z

Authors: S.K.K. Choi, A.V. Kumchev

Published: 2004-12-12T00:06:30.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0412227>)

[PDF](<https://arxiv.org/pdf/math/0412227.pdf>)