On a general density theorem
Volume 214 / 2024
Acta Arithmetica 214 (2024), 389-398
MSC: Primary 11M26; Secondary 11M06
DOI: 10.4064/aa230706-2-3
Published online: 15 April 2024
Abstract
Following the pioneering work of Halász and Turán we prove a general zero-density theorem for a large class of Dirichlet series, containing the Riemann and Dedekind zeta functions. Owing to the application of an idea of Halász (contained in the above mentioned work) and a sharp Vinogradov-type estimate for the Riemann zeta function (due to Heath-Brown) the results are particularly sharp in the neighborhood of the boundary line Re $s=1$.
