arXiv subjects
Publications and source records attributed to Eugenio P. Balanzario.
In this note we consider the distribution of values of weighted sums of the von Mangoldt arithmetical function. By using a formula for the distribution of values of trigonometric polynomials, we are able to present evidence supporting the claim that these weighted sums follow a distribution with a normal-like behavior.
We present a smooth version of Landaus explicit formula for the von Mangoldt arithmetical function. Assuming the validity of the Riemann hypothesis, we show that in order to determine whether a natural number is a prime number, it is sufficient to know the location of a number of non trivial zeros of the Riemann zeta function. Next we use Heisenbergs inequality to support the conjecture that this number of zeros cannot be essentially diminished