The aim of the present paper is to study the relations between the prime distribution and the zero distribution for generalized zeta functions which are expressed by an Euler products and are analytically continued as meromorphic functions of finite order. In this paper, we give an inequality between the order of the zeta function as a meromorphic function and the growth of the multiplicity in ...

In this work, we examine the stationary one-dimensional classical Poisson-Nernst-Planck (cPNP) model for ionic flow – a singularly perturbed boundary value problem (BVP). For the case of zero permanent charge, we provide a complete answer concerning the existence and uniqueness of the BVP. The analysis relies on a number of ingredients: a geometric singular perturbation framework for a reductio...

If f is a meromorphic function in the complex plane, R. Nevanlinna noted that its characteristic function T r, f could be used to categorize f according to its rate of growth as |z| r → ∞. Later H. Milloux showed for a transcendental meromorphic function in the plane that for each positive integer k, m r, f k /f o T r, f as r → ∞, possibly outside a set of finite measure where m denotes the pro...

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f (k) + A(z)f = 0, k ≥ 2, where A(z) is a transcendental meromorphic function with ρp(A) = ρ > 0 and meromorphic functions of finite iterated p−order.

The purpose of the present paper is to introduce new classes of meromorphic spiral-like functions de…ned by using a meromorphic analogue of the Choi-Saigo-Srivastava operator for the generalized hypergeometric function and investigate a number of inclusion relationships of these classes.

We define a p-adic character to be a continuous homomorphism from 1 + tFq [[t]] to Zp. For p > 2, we use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in Zq , indexed by natural numbers relatively prime to p, and for which limi→∞ ci = 0. To such a p-adic character we associate an L-function, and we prove that this L-f...

In the present investigation, the authors derive necessary and sufficient conditions for spirallikeness and convex spirallikeness of a suitably normalized meromorphic p-valent function in the punctured unit disk, using convolution. Also we give an application of our result to obtain a convolution condition for a class of meromorphic functions defined by a linear operator.

In this paper we introduce new subclasses of p-valent starlike, pvalent convex, p-valent close-to-convex and p-valent quasi-convex meromorphic functions and investigate some inclusion properties of these subclasses and investigate various inclusion properties and integral-preserving properties for the p-valent meromorphic function classes.

This paper considers the oscillation on meromorphic solutions of the second-order linear differential equations with the form f'' + A(z)f = 0, where A(z) is a meromorphic function with [p, q]-order. We obtain some theorems which are the improvement and generalization of the results given by Bank and Laine, Cao and Li, Kinnunen, and others.

‎In this paper‎, ‎we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $Q_p$-classes‎. ‎Also‎, ‎these classes are shown to be complete metric spaces with respect to the corresponding metrics‎. ‎Moreover‎, ‎compact composition operators $C_phi$ and Lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $Q_p$-classes are characte...