Multiple zeta functions extend the classical Riemann zeta function to several complex variables by involving multiple summations with distinct exponents. These functions not only encapsulate deep ...

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 ...

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 ...

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 ...

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 ...

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 ...