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On the Primorial Counting Function

2024; Taylor & Francis; Volume: 131; Issue: 5 Linguagem: Inglês

10.1080/00029890.2024.2309123

1930-0972

Christian Axler,

Advanced Mathematical Theories

Let Nk denote the kth primorial and let K(x) be the primorial counting function, the function that counts the number of primorials not exceeding x. In this note, we examine the sign of the functions K(x)−π( log x) and K(x)−li( log x) and find a new necessary and sufficient criterion for the truth of the Riemann hypothesis.