TAILIEUCHUNG - Unicity problem with truncated multiplicities of meromorphic mappings in several complex variales

It is our main purpose of the present paper to present our answers to the above problem. Moreover, they also are remarkable improvements of the results in [TQ2], [DT1], [DT2]. To state some of them, first of all we recall the following. | T¹p chÝ Khoa häc & C«ng nghÖ - Sè 3(43)/N¨m 2007 Unicity problem with truncated multiplicities of meromorphic mappings in several complex variables Pham Hoang Ha (Hanoi National University of Education) Introduction The unicity theorems with truncated multiplicities of meromorphic mappings of into sharing a finite set of q fixed hyperplanes in have the complex projective space received much attention in the last few decades, and they are related to many problems in Nevanlinna theory and hyperbolic complex analysis (see the reference in [A], [TQ1], [TQ2], [DT1], [DT2], [DT3] for the development in related subjects). In the case where multiplicities truncated by 1 or 2, the first results due to H. Fujimoto [Fu] and L. Smiley [S] when q 3N+2, and the recent results due to Thai-Quang [TQ2] and DethloffTan [DT1], [DT2] when 3N-1 q 3N+1. How to say about the unicity theorems with truncated multiplicities in the case where 2N+2 q 3N-1, in particular when q = 2N+2 ? It is our main purpose of the present paper to present our answers to the above problem. Moreover, they also are remarkable improvements of the results in [TQ2], [DT1], [DT2]. To state some of them, first of all we recall the following. Let f be a nonconstant meromorphic mapping of and k a positive integer or k = . Denote by (a) (a For every z ) is the intersection multiplicity of the images of f and H at f(a). , we set Take a meromorphic mapping f of into C, a positive integer d, a positive integer k or k= in into and H a hyperplane in the map of into whose value which is linearly nondegenerate over and q hyperplanes located in general position with dim{ : and consider the set and (f, } n-2 (1 ,k,d) of all meromorphic maps g: i

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