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 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 ...

This article is more than 8 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 ...

Mathematicians attended Roger Apéry’s lecture at a French National Center for Scientific Research conference in June 1978 with a great deal of skepticism. The presentation was entitled “On the ...

Analytic number theory continues to serve as a cornerstone of modern mathematics through its probing study of zeta functions and their applications. At the heart of this discipline is the classical ...

We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local ...

It is known that the Lerch (or periodic) zeta function of nonpositive integer order, l _n (ξ), n Є No := {0,1,2,3,...}, is a polynomial in cot(πξ) of degree n+1. In this paper, a very simple explicit ...

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 ...

A famed mathematical enigma is once again in the spotlight. The Riemann hypothesis, posited in 1859 by German mathematician Bernhard Riemann, is one of the biggest unsolved puzzles in mathematics. The ...

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 ...