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 ...

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 ...

We construct a family of approximations of the Riemann zeta-function and a closely related function formed from finite Euler products, the pole of the zeta-function, and any zeros the zeta-function ...

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 ...

Nous donnons des estimations de type Ω relatives au terme reste dans la formule asymptotique pour le moment d'ordre quatre de la fonction zeta de Riemann et au terme reste dans le problème des ...

Prime numbers, the indivisible atoms of arithmetic, seem to be strewn haphazardly along the number line, starting with 2, 3, 5, 7, 11, 13, 17 and continuing without pattern ad infinitum. But in 1859, ...

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 ...

When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. An unsolved 160-year-old math problem may finally have a solution — but critics are wary. Michael ...

Over the past few days, the mathematics world has been abuzz that Sir Michael Atiyah, the famous Fields Medalist and Abel Prize winner, may have solved the Riemann hypothesis. If his proof turns out ...