Nevanlinna characteristics and defective values of the Weierstrass zeta function

Abstract

In the present paper, we determine the Nevanlinna characteristics of the well-known Weierstrass zeta function ζ(z) , which is closely related to the Weierstrass functions σ(z) and ℘(z) [1]. We also study the problem of defective values of the ζ -function. These problems can be investigated by using the asymptotic formulas from [2, 3], but we use a simpler method. These functions are often used in the investigation of elliptic functions. Note that ζ(z) is a meromorphic function with simple poles Ωmn = 2mω1 + 2nω 2 representable in the form