2022/03/11 by Christian Axler, Axler, Christian
Mathematics · #Analytic Number Theory Research #Mathematical Dynamics and Fractals #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.2203.05917
In this paper we give effective estimates for some classical arithmetic functions defined over prime numbers. First we find the smallest real number x0 so that some inequality involving Chebyshev's ϑ-function holds for every x ≥ x0. Then we give some new results concerning the existence of prime numbers in short intervals. Also we derive new upper and lower bounds for some functions defined over prime numbers, for instance the prime counting function π(x), which improve current best estimates of similar shape.