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 ...

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 ...

The original version of this story appeared in Quanta Magazine. Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the ...

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 Hypothesis is widely regarded as the most important unsolved problem in mathematics. Put forward by Bernhard Riemann in 1859, it concerns the positions of the zeros of the Riemann zeta ...

The Riemann hypothesis is the most important open question in number theory—if not all of mathematics. It has occupied experts for more than 160 years. And the problem appeared both in mathematician ...

Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose ...

Think back to elementary school during which you learned about a seemingly useless mathematical relic called prime numbers. Your teacher told you in class one day that they are special numbers, ...