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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

In this article we will study the spectral properties of a deterministic signal exponentially damped in the past and in the future (the damping in the future is controlled by a time constant). The ...

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 ...