3 papers
math.NT2024
A note on the distribution of clusters and deserts of prime numbers
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 p…
math.NT2023
An explicit formula for the zeros of the Riemann zeta function
Eugenio P Balanzario, Daniel Eduardo Cardenas Romero
We present an explicit formula for a weighted sum over the zeros of the Riemann zeta function. This weighted sum is evaluated in terms of a sum over the prime numbers, weighted wit…
math.NT2023
A smooth version of Landaus explicit formula
Eugenio P. Balanzario, Daniel Eduardo Cardenas Romero, Richar Chacon Serna
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 determ…