The aim of the present paper is to study distributions of singular points of a zeta function which is expressed by an Euler product and is analytically continued as a meromorphic function of finite order. In this manuscript, we give a relation between the growth of the multiplicities for the norms of primitive elements and the order of the zeta function as a meromorphic function.

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented, and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue...

The main purpose of this paper is to study the exceptional values of meromorphic function and its derivative on annulus. We also give some theorems and corollaries about exceptional values of meromorphic function on the annulus, which are the improvement of the previous results given by Chen and Wu.

By applying Ahlfors theory of covering surface, we establish a fundamental inequality of meromorphic function dealing with multiple values in an angular domain. As an application, we prove the existence of some new singular directions for a meromorphic function f, namely a Bloch direction and a pseudo-T direction for f.

We construct the genus two (or two loop) partition function for meromorphic bosonic conformal field theories. We use a sewing procedure involving two genus one tori by exploiting an explicit relationship between the genus two period matrix and pinching modular parameters. We obtain expressions for the partition function for the chiral bosonic string, even rank lattice theories and self-dual mer...

This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. This article is an exposition for non-specialists of Ahlfors’ work in the theory of meromorphic functions. When the domain is not specified we mean meromorphic functions in the complex plane C. The theory of meromorphic functions probably begins with t...

It is well known that an entire function of finite order has an at most countable number of asymptotic values. Gross [I] constructed an example of an entire function of infinite order whose set of asymptotic values coincides with the extended complex plane. Dreisin and Weizmann [2] raised the question of whether there are any restrictions from above on the size of the set of asymptotic values o...

We prove a unicity theorem of Nevanlinna for meromorphic mappings of P into Pm. 1. INTR~DuOTI~N As an application of Nevanlinna’s second main theorem and Borel’s lemma, R. Nevanlinna proved that for any two meromorphic functions in the complex plane @ on which they share four distinct values, then, these two meromorphic functions are the same up to a Mijbius transformation. Since then, there ha...

ABSTRACT. The second fundamental theorem of Nevanlinna concerning meromorphic functions of a complex variable is extended in this note to an analogous result for meromorphic minimal surfaces. A similar extension of the first fundamental theorem involved generalizations of the classical proximity and enumerative functions and also a new visibility function; for the present result, a second enume...