Half-isolated zeros and zero-density estimates

2022/06/23 by Maynard, James, Pratt, Kyle
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2206.11729

Abstract

We introduce a new method to detect the zeros of the Riemann zeta function which is sensitive to the vertical distribution of the zeros. This allows us to prove there are few `half-isolated' zeros. By combining this with classical methods, we improve the Ingham-Huxley zero-density estimate under the assumption that the non-trivial zeros of the zeta function are restricted to lie on a finite number of fixed vertical lines. This has new consequences for primes in short intervals under the same assumption.

Related

• The Alternative Hypothesis for Zeros of the Riemann Zeta-Function
• A remark on density theorems for Riemann's zeta-function
• Zeta Zeros on the Critical Line
• Explicit zero density estimate for the Riemann zeta-function near the critical line
• Constructing a Proof of the Riemann Hypothesis