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 ...

Multiple zeta functions constitute a family of complex-valued functions defined by nested series of the form ζ(s₁,s₂,…,sₖ)=∑_{n₁>n₂>⋯>nₖ>0} n₁^{-s₁} n₂^{-s₂}⋯nₖ^{-sₖ}, where the arguments sᵢ are ...

This article is more than 9 years old. So what? Riemann was interested in the distribution of prime numbers and he discovered a formula for the number of primes less than or equal to a given integer ...

The zeta function of a graph, inspired by analogues in number theory and differential geometry, encodes fundamental cycle and path data in a compact analytic form. Its prototypical instance, the Ihara ...

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 ...