30 research outputs found
Explicit zero density theorems for Dedekind zeta functions
This article studies the zeros of Dedekind zeta functions. In particular, we
establish a smooth explicit formula for these zeros and we derive an effective
version of the Deuring-Heilbronn phenomenon. In addition, we obtain an explicit
bound for the number of zeros in a box.Comment: 24 page
Une region explicite sans zero pour la fonction Zeta de Riemann
The Riemann Zeta function never vanishes in the region : Comment: 32 page
Density results for the zeros of zeta applied to the error term in the prime number theorem
We improve the unconditional explicit bounds for the error term in the prime
counting function . In particular, we prove that, for all , we
have and that, for all , This compares to results of
Platt \& Trudgian (2021) who obtained . Our approach
represents a significant refinement of ideas of Pintz which had been applied by
Platt and Trudgian. Improvements are obtained by splitting the zeros into
additional regions, carefully estimating all of the consequent terms, and a
significant use of computational methods. Results concerning will
appear in a follow up work
Management of stage one and two-E gastric large B-cell lymphoma: chemotherapy alone or surgery followed by chemotherapy?
Management of localized primary gastric B lymphoma (PGL) remains controversial. The aim of this study is to compare two treatments: chemotherapy alone and surgery plus chemotherapy