Author(s)

Dan Liu

Sichuan Normal University, Chengdu, China.

In Riemann’s prime distribution formula, there is a key Riemann ladder function. This is the basis for Riemann to study the distribution of prime numbers. But the calculation of Riemann’s ladder function is very complicated. According to the definition of Riemannian ladder function, we greatly improve the Riemannian ladder function, obtain new ladder function and improved Riemannian prime distribution formula, and prove the improved Riemannian prime distribution formula. We use the improved Riemannian prime distribution formula and merdens theorem to obtain a strong prime theorem.

Ladder Function, Prime Distribution, Metens Theorem, Strong Prime Theorem

Liu, D. (2021) Improved Riemann Ladder Function. Journal of Applied Mathematics and Physics, 9, 584-593. doi: 10.4236/jamp.2021.94042.