Uniqueness of meromorphic functions sharing a set in annuli. Click download or read online button to meromorphic functions and analytic curves book pdf for free now. Complex analysis, notes 2 meromorphic functions and. Furthermore, is meromorphic on the extended complex plane if and only if there exists such that for. Catanese unioersit di pisa universit di pisa pisa, italy pisa, italy w introduction let f be a meromorphic function on c. To this end it develops fundamental methods of multivariable complex analysis that reach far beyond the applications we are going to give here. Does knowing the file type of an encrypted file make. Weighted sharing and uniqueness of meromorphic functions volume 161 indrajit lahiri please note, due to essential maintenance online transactions will not be possible between 02. This theory has proved a tool of unparallelled precision for the study of the roots of equations fz a, f1z b, etc.
Entire and meromorphic functions pdf for free, preface. Meromorphic functions download ebook pdf, epub, tuebl, mobi. On entire and meromorphic functions that share one small. On the iterations and the argument distribution of.
Zeros and poles of some meromorphic 1forms on the riemann sphere. Langley october 9, 2018 in fondest memory of gunter frank and milne anderson abstract the paper determines all meromorphic functions f in csuch that fand f have. Meromorphic functions of several complex variables. For a meromorphic function f, we use the following notation. Download pdf meromorphic functions and analytic curves.
The set of poles of coincides with the discrete set and if. Nevanlinna theory, meromorphic function, uniqueness theorem 30d35 2000 mr subject classification 1 introduction in this paper, meromorphic function means meromorphic in the complex plane c. Entire and meromorphic functions mathematisches seminar. If in addition all critical points of the function are multiple, then a. In this paper a meromorphic function means a function that is meromorphic in the whole complex plane. It is assumed that the reader is familiar with the notations of the nevanlinna theory see, for example, 1. Langley skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. Meromorphic function a function that can be represented in the form of a quotient of two entire functions, that is, the quotient of the sums of two. Representations of meromorphic functions there are two natural ways to represent a rational function. Let be a nonconstant meromorphic function, then lemma 14 see.
Examples of meromorphic functions that share four or ve pairs of values are discussed. Meromorphic function on riemann surface mathematics. Meromorphic functions that share one small function cm or im. In complex analysis, a meromorphic function on an open subset d of the complex plane is a function that is holomorphic on all d except a set of isolated points, which are poles for the function subcategories. The growth of a meromorphic function with exceptional values 238 6. Such a function will still be wellbehaved, except possibly at the points where the denominator of the fraction is zero. Some results on uniqueness of meromorphic functions sharing a. We shall develop in this course nevanlinnas theory of meromorphic functions. For example, my favorite theorem in all of mathematics is a theorem of r.
Jan 22, 2016 in the mathematical field of complex analysis, a meromorphic function on an open subset d of the complex plane is a function that is holomorphic on all d except a set of isolated points the poles. We assume the reader is familiar with the nevanlinna theory of meromorphic functions. The classical representation problem for a meromorphic function f in cn, n1, consists in representing f as the quotient fgh of two entire functions g and. Pdf research questions on meromorphic functions and complex. Meromorphic functions that share four or ve pairs of values. Covering properties of meromorphic functions, negative. The function has an essential singularity at if and only if the laurent expansion of about has infinitely many negative terms.
Meromorphic definition of meromorphic by merriamwebster. Meromorphic function, small function, uniqueness theorem. If this is the first time you use this feature, you will be asked to authorise cambridge core to connect with your account. It has a removable singularity if and only if degq degp. Click download or read online button to get meromorphic functions book now.
This chapter presents the analogues of the mittagleffler and weierstrass theorems for functions of several complex variables. Some books on specific topics in the theory of meromorphic functions published after 1970. Meromorphic functions representable by series of simple fractions 252 chapter 6. Entire and meromorphic functions pdf books library land.
Introduction in this paper a meromorphic function means meromorphic in the whole complex plane. This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Let where and are two nonconstant meromorphic functions. Recall that a rational function on c is a function of the form rz pz qz where both pz and qz are polynomials. In the mathematical field of complex analysis, a meromorphic function on an open subset d of the complex plane is a function that is holomorphic on all of d except for a set of isolated points, which are poles of the function. Meromorphic functions sharing a small function wang, songmin and. The representation of a meromorphic function as the quotient. Ostrovskii polyanalytic functions and their generalizations m. Let be a nonconstant entire function and be a meromorphic function such that and as. Conversely, every holomorphic mapping, defines a meromorphic function in. Our discussion here can be repeated in the future for a meromorphic function with z0 as a pole.
Mathematics is a beautiful subject, and entire functions is its most beautiful. Intuitively, a meromorphic function is a ratio of two wellbehaved holomorphic functions. One is to express it as a quotient of two polynomials, the other is to use partial fractions. This is an appendix to the english translation of the book by a. In this paper, the term meromorphic will always mean meromorphic in the complex plane c. We have defined the nevalinna characteristic function of a meromorphic function. A lower bound for the number of zeros of a meromorphic. Weighted sharing and uniqueness of meromorphic functions. However that may lead to some inconveniences, as pointed out in my question can a meromorphic function have removable singularities so its reasonable to consider removable singularities in the definition of meromorphic function. Does knowing the file type of an encrypted file make it easier to decrypt. Value distribution of the kth derivatives of meromorphic. Balk the first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications.
Every meromorphic function defines a continuous mapping of the domain into the riemann sphere, which is a holomorphic mapping relative to the standard complex structure on. Zeros of the derivative of a padic meromorphic function and applications boussaf, kamal, escassut, alain, and ojeda, jacqueline, bulletin of the belgian mathematical society simon stevin, 2012. Let be a nonconstant meromorphic function and a meromorphic function such that, and do not have any common pole and as. Pdf in this paper, we obtain a quasinormal criterion of meromorphic functions and give an example of an application in the value distribution theory find. Nevanjinna that two functions, meromorphic in the whole complex plane, that share five values must be. Entire or meromorphic functions sharing one value sciencedirect. Meromorphic functions that share one small function cm or. What happens to the values of the meromorphic function fr as z approaches a pole. Nevanlinna mentioned that, to his knowledge, no melhod for the solution of the.
Download pdf meromorphic functions and analytic curves free. Meromorphic function on riemann surface mathematics stack. Meromorphic functions whose derivatives share small functions li, ping and zhang, yi, kodai mathematical journal, 2004. Representing a meromorphic function as the quotient. Feb 12, 2011 the function has an essential singularity at if and only if the laurent expansion of about has infinitely many negative terms. In the mathematical field of complex analysis, a meromorphic function on an open subset d of. Meromorphic functions and analytic curves download meromorphic functions and analytic curves ebook pdf or read online books in pdf, epub, and mobi format. Meromorphic functions and analytic curves, issue 12, hermann weyl, 1943, mathematics, 269 pages. The first three results follow immediately from the previous section. A lower bound for the number of zeros of a meromorphic function and its second derivative.
From this, we look at linear subspaces of meromorphic 0forms and 1forms generated on riemann surfaces and prove the riemannroch theorem, which gives us an algebraic description of meromorphic functions from riemann surfaces. The representation of a meromorphic function as the. Research questions on meromorphic functions and complex differential equations article pdf available in computational methods and function theory 17. Pdf a quasinormal criterion of meromorphic functions and its. Value distribution with respect to the arguments 261 1. The main conjecture of this paper, which is discussed in greater detail in chapter 4, is conjecture 1. If f is such a function, denote by ff the fatou set of f and jf the julia set of f. In complex analysis, a meromorphic function on an open subset d of the complex plane is a function that is holomorphic on all d except a set of isolated points, which are poles for the function. Further, some examples are given to show that the conclusions are meaningful. The term comes from the ancient greek meros, meaning part every meromorphic function on d can be expressed as the ratio between two holomorphic functions with. Covering properties of meromorphic functions, negative curvature and spherical geometry m. A possible fix to the definition of meromorphic function one without considering too many cases is the following. Introduction to the theory of entire functions of several variables, lev isaakovich ronkin, 1974. Meromorphic definition is relating to or being a function of a complex variable that is analytic everywhere in a region except for singularities at each of which infinity is the limit and each of which is contained in a neighborhood where the function is analytic except for the singular point itself.
We say that a is small with respect to f if tar otfr as r denote by rf the set of all meromorphic functions on c which are small with respect to f. Growth of meromorphic function sharing functions and some. Meromorphic definition of meromorphic by the free dictionary. In this paper, we prove that two nonconstant meromorphic functions are identical provided that they share five distinct small functions im in some angular domains. Meromorphic functions of several variables springerlink. Value distribution of meromorphic functions anatoly. In 2009, zhang and yang 15 further improved the above result in the. Some results on uniqueness of meromorphic functions. A rational function has a pole or removable singularity at in nity. Download meromorphic functions and analytic curves ebook pdf or read online books in pdf, epub, and mobi format. For a meromorphic function a on c with reduced representation a a0. Meromorphic functions sharing a small function wang, songmin and gao, zongsheng, abstract and applied analysis, 2007 meromorphic functions that share some pairs of small functions li, ping and yang, chungchun, kodai mathematical journal, 2009. Uniqueness of meromorphic functions sharing a set in annuli scielo. In the mathematical field of complex analysis, a meromorphic function on an open subset d of the complex plane is a function that is holomorphic on all.
Let a i l be a third root of unity and let 7 be a nonconstant entire function. It is assumed that the reader is familiar with the notations of nevanlinna theory of meromorphic functions, for instance, t r, f, n r, f, m r, f, n. An entire function fcan also be considered as a meromorphic function f. A power of a meromorphic function sharing one value with its derivative sujoy majumder communicated by vasile br nzanescu let fbe a nonconstant meromorphic function, n, kbe two positive integers and az6 0. A lower bound for the number of zeros of a meromorphic function and its second derivative volume 39 issue 1 j. Let be a domain in or an dimensional complex manifold and let be a complex analytic subset of codimension one or empty. This site is like a library, use search box in the widget to get ebook that you want. Estimating the growth of meromorphic solutions has been an important topic of research in complex differential equations. For a nonzero meromorphic function f on c with reduced representation f f0. Let f be a nonconstant meromorphic function, and let a n. Then every solution of 3 is meromorphic in the plane, and if u.
Considering the uniqueness of meromorphic functions concerning differential monomials,we obtain that, if two nonconstant meromorphic functions fz and gz satisfy,where k and n are tow positive integers satisfying k. The work of the third author was supported by jsps kakenhi grant numbers 16k05194 and 254001. Eremenkoy december 3, 1999 abstract every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan p 8. In this paper, we devoted to considering uniqueness problems by estimating the growth of meromorphic functions. Ostrovskii, distribution of values of meromorphic functions, moscow, nauka. A holomorphic function defined on is called a meromorphic function in if for every point one can find an arbitrarily small neighbourhood of in and functions holomorphic in without common noninvertible factors in. Pdf in this paper we mainly estimate the hyperorder of an entire function which shares one function with its derivatives. How can you reconcile this with the inequality fr le 1. Meromorphic functions article about meromorphic functions. Pdf research questions on meromorphic functions and. Meromorphic functions include many important functions and classes of functions rational functions, trigonometric functions, elliptic functions, the gamma function, the zeta function. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. Pdf hyperorder and order of meromorphic functions sharing. Nevanjinna that two functions, meromorphic in the whole complex plane, that share five values must be identical.