arXiv subjects

Daniel Eduardo Cardenas Romero

Publications and source records attributed to Daniel Eduardo Cardenas Romero.

2 recordsLinked to original sources

arXiv2023

An explicit formula for the zeros of the Riemann zeta function

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 with help of the Hermite polynomials. From the explicit formula presented in this note, it follows that prime numbers determine the distribution of the zeros of the Riemann zeta function. In fact, it is possible to compute the zeros of the zeta function without actually using this function.

math.NT↗

arXiv2023

A smooth version of Landaus explicit formula

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

math.NT↗