Values of twisted Barnes zeta functions at negative integers

Bayad A., ŞİMŞEK Y.

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, vol.20, no.2, pp.129-137, 2013 (SCI-Expanded) identifier identifier


In this paper, we study analytical and arithmetical properties of the twisted zeta function , where a"e(s) > N, a"e(x) > 0, w a a",\{0}, N a a"currency sign, and a (1), aEuro broken vertical bar, a (N) have positive real parts. These functions have many interesting properties. We prove a collection of fundamental identities satisfied by zeta functions of this kind. For instance, special values of these zeta functions are related to twisted Barnes numbers and polynomials. This gives us a new elementary approach to new and known results concerning the Barnes zeta functions. In particular, we derive some well-known results on the Hurwitz zeta functions.