论文标题
半分离的零和零密度估计值
Half-isolated zeros and zero-density estimates
论文作者
论文摘要
我们引入了一种新方法来检测Riemann Zeta函数的零，该ZETA函数对零的垂直分布敏感。这使我们能够证明几乎没有“半隔离”零。通过将其与经典方法相结合，我们在假设Zeta函数的非平凡零仅限于有限数量的固定垂直线的假设下，改善了Ingham-Huxley零密度估计值。在相同的假设下，这对素数有新的后果。
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.
