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 hypothesis raised in 1859 is one of the six unsolved Millennium problems, and its proof will greatly facilitate the understanding of the distribution laws of prime numbers. For a long time ...

This article is more than 8 years old. So what? Riemann was interested in the distribution of prime numbers and he discovered a formula for the number of primes less than or equal to a given integer ...

We characterize the nonreal zeros of the Riemann zeta function and their multiplicities, using the "asymptotic convergence degree" of "improper Riemann sums" for elementary improper integrals. 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 ...

I. The Montgomery-Odlyzko Law tells us that the non-trivial zeros of the Riemann zeta function look like—statistically, that is—the eigenvalues of some random Hermitian matrix. The operators ...

Numbers like π, e and φ often turn up in unexpected places in science and mathematics. Pascal’s triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there’s the ...