Abstract
In this paper we give new estimates for integrals involving some arithmetic functions defined over prime numbers. The main focus here is on the prime counting function $\pi(x)$ and the Chebyshev $\vartheta$-function. Some of these estimates depend on the correctness of the Riemann hypothesis on the nontrivial zeros of the Riemann zeta function $\zeta(s)$.
Citation
Christian Axler. "New estimates for some integrals of functions defined over primes." Funct. Approx. Comment. Math. 68 (2) 207 - 229, June 2023. https://doi.org/10.7169/facm/2049
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