ABOUT THE RADIUS OF CONVERGENCE OF THE ZETA FUNCTION OF AN ADDITIVE ARITHMETICAL SEMIGROUP
Richard Warlimont · Quaestiones Mathematicae · 2001
Let (G, ∂) be an additive arithmetical semigroup in John Knopfmacher's sense with f(n), g(n) denoting the number of all elements, prime elements of G with degree ∂ = n. It is shown that if lim sup g(n)/f(n) < 1 then the zeta function of (G,∂) which is a power series has a n→∞ positive radius of convergence.