In this article we will study the spectral properties of a deterministic signal exponentially damped in the past and in the future (the damping in the future is controlled by a time constant). The ...

The Riemann zeta function, a central object in analytic number theory, has long intrigued mathematicians and physicists alike. Its non-trivial zeros not only encapsulate the distribution of prime ...

It was a good week for physics research as a team from Virginia Tech made a heat discovery that expanded on an 18th-century principle involving ice placed on a hot surface—Jonathan Boreyko and Mojtaba ...

This is a preview. Log in through your library . Abstract Assuming the Riemann Hypothesis, we prove that a positive proportion of the time, the gap between consecutive zeros of the Riemann ...

The functional equation for $\zeta(s)$ is used to obtain formulas for all derivatives $\zeta^{(k)}(s)$. A closed form evaluation of $\zeta^{(k)}(0)$ is given, and ...

Prime numbers are maddeningly capricious. They clump together like buddies on some regions of the number line, but in other areas, nary a prime can be found. So number theorists can’t even roughly ...