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 ...

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 ...

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 ...

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 ...

This is a preview. Log in through your library . Abstract Assuming the Riemann Hypothesis, we prove that a positive proportion of the time, the gap between consecutive zeros of the Riemann ...

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 ...

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 ...

Think back to elementary school during which you learned about a seemingly useless mathematical relic called prime numbers. Your teacher told you in class one day that they are special numbers, ...