Sign changes in the prime number theorem

Let V (T) denote the number of sign changes in psi(x) - x for x is an element of [1, T]. We show that lim inf(T ->infinity) V (T)/log T >= gamma(1)/pi + 1.867 . 10(-30), where gamma(1) = 14.13... denotes the ordinate of the lowest-lying non-trivial zero of the Riemann zeta-function. This improves on a long-standing result by Kaczorowski.

Automated summary

By analyzing the number of sign changes in ψ(x) - x, we have proven a new mathematical inequality that improves upon a long-standing result by Kaczorowski, revealing important properties related to the zeros of the Riemann zeta function.