Asymptotic relations between interpolation differences and zeta functions

Abstract

Asymptotic relations between zeta functions (such as, ζ(s),β(s), and other Dirichlet L-functions) and interpolation differences of functions like |y|s and their interpolating entire functions of exponential type 1 are discussed. New criteria for zeros of the zeta functions in the critical strip in terms of integrability of the interpolation differences are obtained as well.