Half-isolated zeros and zero-density estimates

James Maynard; Kyle Pratt

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arXiv · 2206.11729

Half-isolated zeros and zero-density estimates

James Maynard·Kyle Pratt

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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.

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James Maynard, Kyle Pratt. 2022-06-23. Half-isolated zeros and zero-density estimates. https://arxiv.org/abs/2206.11729

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