A new zero‐density estimate for ζ(s) and the error term in the prime number theorem
Abstract
Abstract We will provide a new type of zero‐density estimate for when is sufficiently close to 1. In particular, we will show that can be bounded by an absolute constant when is sufficiently close to the left edge of the Korobov–Vinogradov zero‐free region. As a consequence, we show that where is a decreasing function such that for . This is an essentially optimal refinement of a result due to Pintz, who showed that for any .
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Harmonic Analysis Research
Mathematical Approximation and Integration
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN