The Riemann Hypothesis remains one of mathematics’ most enduring and influential conjectures, proposing that all nontrivial zeros of the Riemann zeta function lie on the critical line where the real ...

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 ...

Dans sa preuve du théorème d'Apéry sur l'irrationalité de ζ(3), Beukers [B] a introduit des intégrales doubles et triples de fonctions rationnelles donnant de bonnes suites d'approximations ...

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 ...

Yitang Zhang, a number theorist at the University of California, Santa Barbara, has posted a paper on arXiv that hints at the possibility that he may have solved the Landau-Siegel zeros conjecture.

Numbers like pi, e and phi 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 ...

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 ...

Researchers have made what might be new headway toward a proof of the Riemann hypothesis, one of the most impenetrable problems in mathematics. The hypothesis, proposed 160 years ago, could help ...