By Tahir Aliyev Azeroglu, Promarz M. Tamrazov
This quantity gathers the contributions from impressive mathematicians, akin to Samuel Krushkal, Reiner Kühnau, Chung Chun Yang, Vladimir Miklyukov and others.It may help researchers to resolve difficulties on complicated research and power concept and talk about numerous functions in engineering. The contributions additionally replace the reader on fresh advancements within the box. additionally, a unique a part of the amount is totally dedicated to the formula of a few vital open difficulties and engaging conjectures.
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Extra info for Complex Analysis and Potential Theory: Proceedings of the Conference Satellite to ICM 2006
4. Mohon’ko, A,, The Nevanlinna characteristics of certain meromorphic functions, Teor. Funktsi? Funktsional. Anal. , 14(1971), 83-87. 5. Mues, E. , The theorem of Tumura-Clunie for meromorphic function, J. London Math. ,23(1981), no. 2, 113-122. 6. , The second main theorem for small functions and related problems, Acta Math. 192(2004), no. 2, 225-294. 7. , The second main theorem for small functions and related problems, Acta Math. 192(2004), no. 2, 225-294. 8. -C. , Quantitative estimations on the zeros of differential polynmials, Science in China, Series A , 1(1993), no.
From (50), we see that the multiplicity of any zero of f - Xjal is at least k / d j . Since k and n are maturely prime, the multiplicity of any pole of f is at least k . By Nevanlinna’s second fundamental theorem, we have + + 1 1 1 + + 1 + which implies k 5 d l d2 1. Since p1 p2 = n < k and d j 5 pj , we have n < k 5 n + l . Therefore, k = n + l . If d l < p1 or d2 < p2, then d1+d2 < p1+p2 = n, which yields k 5 n, a contradiction t o the assumption. Hence d i = p j , j = 1,2. Without loss of generality, we assume d l 5 d2.
Alf + ao, a, Z0. If and if f and g satisfy the following functional equation: then P ( f ) assumes one of the form described in Theorem A . Corollary 2. , a, be given meromorphic functions. ,a, being its small functions, and P ( f ) E P is as defined in Corollary 1. If there exist a positive integer k > 2n and a nonconstant meromorphic function g satisfying the functional equation: then Remark. The condition k > 2n in Corollary 2 is necessary. For example, let h be the elliptic function which satisfy (h')2= 4h3 + 6h2 4h + 1, and let g = 1 l / h , f = h'/h2,then g4 = f 2 - 1.
Complex Analysis and Potential Theory: Proceedings of the Conference Satellite to ICM 2006 by Tahir Aliyev Azeroglu, Promarz M. Tamrazov