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 ...

American Journal of Mathematics, Vol. 124, No. 1 (Feb., 2002), pp. 1-48 (48 pages) We consider zeta functions defined as Euler products of $W(p,p^{-s})$ over all ...

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 ...

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 ...

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 ...

Forbes contributors publish independent expert analyses and insights. So what? Riemann was interested in the distribution of prime numbers and he discovered a formula for the number of primes less ...

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 ...

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 ...

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 ...