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 ...

The patterns in the primes trace back to an 1859 hypothesis involving the legendary Riemann zeta function. Mathematician ...

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 ...

American Journal of Mathematics, Vol. 124, No. 1 (Feb., 2002), pp. 1-48 (48 pages) We consider zeta functions defined as Euler products of $W(p,p^{-s})$ over all ...

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 ...

Prime numbers, the indivisible atoms of arithmetic, seem to be strewn haphazardly along the number line, starting with 2, 3, 5, 7, 11, 13, 17 and continuing without pattern ad infinitum. But in 1859, ...

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 ...

This is a preview. Log in through your library . Abstract Louis Solomon introduced the notion of a zeta function $\zeta_\Theta(s)$ of an order $\Theta$ in a finite ...