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 ...

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 ...

But it’s the functional equation that sets the stage for focusing on zeroes of the Riemann zeta function with Re ( s) = 1 / 2 … and then the Riemann Hypothesis! So it’s worth thinking about. Hope ...

Analytic properties of three types of multiple zeta functions, that is, the Euler-Zagier type, the Mordell-Tornheim type and the Apostol-Vu type have been studied by a lot of authors. In particular, ...

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 ...

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 ...

Did a team of mathematicians just take a big step toward answering a 160-year-old, million-dollar question in mathematics? Maybe. The crew did solve a number of other, smaller questions in a field ...