Riemann hypothesis and some new integrals connected with the integral negativity of the remainder in the formula for the prime-counting function $π(x)$

Details Riemann hypothesis and some new integrals connected with the integral negativity of the remainder in the formula for the prime-counting function $π(x)$ Riemann hypothesis and some new integrals connected with the integral negativity of the remainder in the formula for the prime-counting function $π(x)$

2011-05-25

arxiv.org/abs/1105.4945v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In this paper a new integral for the remainder of $\pi(x)$ is obtained. It is
proved that there is an infinite set of the formulae containing miscellaneous
parts of this integral.

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