Tauberian theorems with applications to arithmetical semigroups and probabilistic combinatorics
K.-H. Indlekofer · Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae Sectio computatorica · 2011
In this paper we investigate functions Z and F holomorphic in the unit disk {y ∈ C : |y| < 1}, which can be representedm y m , respectively, where λ(m) ∈ R ≥0 and λ f (m) ∈ C for all m ∈ N. We define a class F of functions Z and characterize the asymptotic behaviour of the quotient f (n)/γ(n) as n → ∞ if, for example, |λ f | ≤ λ.The results are applied to the generating functions of additive arithmetical semigroups and of exp-log schemas in combinatorics.We notice that the definition of the functions Z ∈ F does not require any analytic continuation of Z(y) over the boundary |y| = 1.