By using the second main theorem of the meromorphic function on annuli, we investigate the problem on two meromorphic functions partially sharing five or more values and obtain some theorems that improve and generalize the previous results given by Cao and Yi.

The main concerned target of this article is to define and study some classes meromorphic function spaces using the general spherical derivatives. Besov-type functions as well normal are considered intensively both compared deeply with each other. Specifically, multiple results concerning meromorphic-type non-normal obtained by help proved constructing specific mild conditions on sequences poin...

It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...

We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is CP1 and the function is a polynomial, we give an elementary way of finding this number. In the general case, we show that, as the multiplicities of critical points tend to infinity, the asymptotic for the number of ...

‎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...

The quantum Rabi model (QRM) is widely recognized as an important in systems, particularly optics. Hamiltonian $H_{\text{Rabi}}$ known to have a parity decomposition $H_{\text{Rabi}} = H_{+} \oplus H_{-}$. In this paper, we give the explicit formulas for propagator of Schr\"odinger equation (integral kernel time evolution operator) and $H_{\pm}$ by Wick rotation (meromorphic continuation) corre...

where I is a finite set of distinct tuples (α0,α1, . . . ,αk) for which eachαi is a nonnegative integer, and the aᾱ are meromorphic functions in D = {z | |z| < 1}. For some index sets I, we determine conditions on aᾱ, whereby a meromorphic solution f of (1.1) in D will have finite order of growth as measured by the Ahlfors-Shimizu characteristic function. In [1], Bank investigated (1.1) where I...

Nevanlinna theory [Ne] was created to give a quantitative measure of the value distribution for meromorphic functions, for instance to measure the extent to which they approximate a finite number of points. We view a meromorphic function as a holomorphic map ƒ : C —• P into the projective line. The theory has various higher dimensional analogues, of which we shall later consider maps ƒ : C —• X...

We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on the comparison of two characteristic cycles and uses a combinatorial description due to Àlvarez-Montaner, Garćıa–López and Zarzuela of the characteristic cycle of the D...