A generalization of the riemann zeta-function

Abstract

A generalization of the Riemann zeta-function which has the form

$$\zeta _\alpha (s) = \prod\limits_p {\frac{1}{{1 - p^{ - s} + (p + a)^{ - 3} }}} $$

is considered. Analytical properties with respect to s and asymptotic behaviour whena → ∞ are investigated. The correspondingL-function is also discussed. This consideration has an application in the theory ofp-adic strings.