One is to express it as a quotient of two polynomials, the other is to use partial fractions. By collecting results from the previous section, we are immediately led to the following proposition regarding the laurent expansions of complex valued functions. Many results included in the book belong to the authors, and were previously available only in journal articles. We shall develop in this course nevanlinnas theory of meromorphic. Thus our book can be thought of as a modest effort to expose parts of the known theory of meromorphic functions. A riemann surface is a geometric object that is locally modeled on the complex plane. Let f be a transcendental meromorphic function of order less than one. These results extend the related results obtained by chen and shon.
The function tr,f is called the characteristic function of f z. Uniqueness of meromorphic functions sharing one value volume 85 issue 2 chun wu, chunlai mu, jiangtao li. Uniqueness of a meromorphic function f n and its difference operator with the same 1points and poles is also proved. Lectures on the theory of functions of several complex variables by b. Meromorphic functions and residues q what are we going to discuss today. In this paper, we have investigated the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing a small function. Generalization of uniqueness of meromorphic functions. Remark if f satis es the mean property, then holomorphic forms on a riemann surface m, denoted by h m, are those. Shtffman 4, lemma 3 has obtained the following result concerning remov able singularities of analytic functions of several complex variables. The authors prove that the exact difference has infinitely many fixed points, if and are borel exceptional values or nevanlinna deficiency values of f.
Links to pubmed are also available for selected references. Bookmark file pdf complex analysis by ponnusamy free. For example, the equation this example shows that for the linear difference equation with meromorphic coefficients, the condition. Let a i l be a third root of unity and let 7 be a nonconstant entire function.
In addition to elementary functions like the exponent, cosine and tangent, this class includes higher transcendental functions, indispensable in physics and engineering. We shall develop in this course nevanlinnas theory of meromorphic functions. Fixed points of difference operator of meromorphic functions. Meromorphic functions constitute the most basic class of functions used in mathematics and most of its applications. In this paper, with the aid of weighted value sharing we study the uniqueness problems of meromorphic functions when certain nonlinear differential polynomials generated by them share a nonconstant polynomial with weight two. Prove that every meromorphic function on c is the quotient of two entire functions. A meromorphic function is a singlevalued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to. As a rst try, one might consider fz x k p k 1 z b k. The notation is defined to be any quantity satisfying as possibly outside a set of of finite linear measure let be a family of meromorphic functions on a domain. Download fulltext pdf download fulltext pdf on meromorphic functions defined by a new operator containing the mittagleffler function article pdf available in symmetry 112. Furthermore, is meromorphic in the extended complex plane if is either meromorphic or holomorphic at.
If and have the same zeros with same multiplicities ignoring multiplicities, then we say that and share cm im. On growth of meromorphic solutions for linear difference. Some normality criteria of meromorphic functions journal. Fixed points of composite meromorphic functions and normal. In this paper we extend the notions of holomorphic and meromorphic 1forms from the. Entire and meromorphic functions polyanalytic functions and their generalizations. Though this is a classical subject and much is known about meromorphic functions, we felt that an accessible exposition was lacking in the current literature. We prove four uniqueness theorems for meromorphic functions f and g sharing values 0, 1, 1which improve results of i. In this paper we introduce and investigate a certain subclass of functions which are analytic in the punctured unit disk and meromorphically closetoconvex. This site is like a library, use search box in the widget to get ebook that you want. We study the uniqueness of meromorphic functions that share one small function with more general differential polynomial. There is another way to think of meromorphic functions. Meromorphic functions that share fixedpoints mingliang fang1 state key laboratory of millimeter wa es, southeast uni ersity, nanjing 210096, peoples republic of china email. Proving that meromorphic on the extended plane implies polynomial.
The value distribution theory of meromorphic functions occupies one of the central places in complex analysis which now has been applied to complex dynanics, complex differential and functional equations, diophantine equations and others. Introduction to the theory of entire functions of several variables, lev isaakovich ronkin, 1974. On meromorphic functions that share one small function of. These functions, and their additive counterparts known as rigid meromorphic period functions of weight two, are reminiscent of the \rational period functions that are studied in kn, ash, cz, and can be classi ed along similar lines. Available formats pdf please select a format to send. In several complex variables, a meromorphic function is defined to be locally a quotient of two holomorphic functions. A before starting a new topic, let us recall what we did so far. Entire and meromorphic functions pdf for free, preface. Let be a domain in or an dimensional complex manifold and let be a complex analytic subset of codimension one or empty. In this article, we investigate the uniqueness problems of difference operators of two meromorphic functions. Uniqueness of meromorphic functions sharing three values arindam sarkar1 and paulomi chattopadhyay2 abstract. Meromorphic functions sharing a small function wang, songmin and gao.
We shall use the standard notations in nevanlinnas value distribution theory of meromorphic functions such as, and see, e. Ostrovskii polyanalytic functions and their generalizations m. Pdf hyperorder and order of meromorphic functions sharing. Meromorphic functions that share one small function cm or im with their first derivative amer h. On the isomorphism theorem of the meromorphic function fields dedicated to professor kentaro murata on his 60th birthday takao kato received august 18, 1981 1. Entire and meromorphic functions pdf books library land. Covering properties of meromorphic functions, negative curvature and spherical geometry m. Mathematica volumen 4, 197811979, 145149 an extension tieorem for meromorphic functions of several variables juhani riihentaus 1. Meromorphic functions of several complex variables. Malgrange notes by raghavan narasimhan distributed for the tata institute of fundamental research.
Full text full text is available as a scanned copy of the original print version. Let f and g be two nonconstant meromorphic functions. Picard set and cannot be the union of all the zeros and ones of any entire function. Then every solution of 3 is meromorphic in the plane, and if u.
Get a printable copy pdf file of the complete article 194k, or click on a page image below to browse page by page. Alkhaladi department of mathematics college of science diyala university, baquba, iraq email. Some results on uniqueness of meromorphic functions. A meromorphic function is called a small function with respect to if, that is, as possibly outside a set of finite linear measure. In the mathematical field of complex analysis, a meromorphic function on an open subset d of. Meromorphic functions and projective curves mathematics. A selfcontained exposition of the inverse problem for meromorphic functions of finite order with finitely many deficiencies is given in full detail. Some books on specific topics in the theory of meromorphic functions published after 1970. Pdf in this paper we mainly estimate the hyperorder of an entire function which shares one function with its derivatives. Hayman studied the value distribution of certain meromorphic functions and. Includes bibliographical references and indexes entire and meromorphic functions a.
Get a printable copy pdf file of the complete article 715k. Langley september 2, 2016 in fondest memory of gunter frank and milne anderson abstract the paper determines all meromorphic functions f in csuch that fand f have. In this paper, we study the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing fixed point and obtain some results which generalize the results due to subhas s. Meromorphic functions and analytic curves, issue 12, hermann weyl, 1943, mathematics, 269 pages.
Function field and meromorphic functions on a riemann surface 2 show that a space of holomorphic sections of a line bundle is isomorphic to the space of meromorphic functions on a riemann surface. Pdf in this paper we study some growth properties of entire and meromorphic functions to generalise some earlier results. Lectures on the theory of functions of several complex. Meromorphic forms on riemann surface structures shankara pailoor abstract.
Pmc free article articles from proceedings of the national academy of sciences of the united states of america are provided here courtesy of national academy of sciences. 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, a meromorphic functions mean meromorphic in the whole complex plane. If in addition all critical points of the function are multiple, then a. 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. This theory has proved a tool of unparallelled precision for the study of the roots of equations fz a, f1z b, etc. Pdf on uniqueness of two meromorphic functions sharing a. Thus, if d is connected, the meromorphic functions form a field, in fact a field extension of the complex numbers. On a result of ueda concerning unicity of meromorphic functions alzahary, thamir c. Covering properties of meromorphic functions, negative. Unicity theorems for meromorphic functions that share.
Fixed points of composite meromorphic functions and normal families volume 4 issue 4 walter bergweiler. In this case we say that has a pole or is holomorphic at infinity. On certain subclass of meromorphic closetoconvex functions. Introduction it is one of beautiful theorems in classical function theory that compact riemann surfaces are determined by the fields of functions meromorphic on them. Certain meromorphic functions sharing a nonconstant polynomial with their linear polynomials li, xiaomin and yi, hongxun, bulletin of the belgian mathematical society simon stevin, 2014. Representations of meromorphic functions there are two natural ways to represent a rational function. As corollaries, we obtain results which answer open questions posed by yu 2003. The object is to do the same for meromorphic functions. Introduction the value distribution theory of meromorphic functions occupies one of the central places in complex analysis. Let a n be its poles, listed according to their order. Pdf on meromorphic functions defined by a new operator. We have defined the nevalinna characteristic function of a meromorphic function fz. 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. Unicity of meromorphic functions related to their derivatives han, qi and hu, peichu, bulletin of the belgian mathematical.
Keywords entire functions, uniqueness, meromorphic functions, fixed point, differential polynomials. Differential independence of meromorphic functions. The space of meromorphic di erentials is denoted by m m 2. A meromorphic function a is called a small function with respect to f, provided that t ra s r f. Meromorphic functions that share one small function cm or. Uniqueness of difference operators of meromorphic functions. Winding numbers and meromorphic functions explained. Content distributed via the university of minnesotas digital conservancy may be subject to additional license and use restrictions applied. We show that if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points then it is. Click download or read online button to get meromorphic functions book now. Let be a nonconstant meromorphic function in the complex plane.
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