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 ...

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 ...

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.

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 ...

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

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, ...

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 ...