Conditional mean values of long Dirichlet polynomials
Abstract
Abstract Conditionally on the Riemann hypothesis we prove asymptotic formulae for mean values of various long Dirichlet polynomials involving the von Mangoldt function. A key feature of our methods is that they bypass the use of strong twin-prime like conjectures for correlation sums. We also give new large deviation estimates for long Dirichlet polynomials over primes.
Fields of Study & Subjects
Analytic Number Theory Research
Meromorphic and Entire Functions
Analytic and geometric function theory
Publication details
- Journal / source
- Forum Mathematicum
- Publisher
- Walter de Gruyter GmbH
- Publication date
- 29 July 2026
- Language
- EN