| Co-Investigator(Kenkyū-buntansha) |
NOGUCHI Junjiro Tokyo University, Graduate School of Mathematical Science, Professor, 数理科学研究科, 教授 (20033920)
IWASE Junichi Kanazawa University, Faculty of Science, Assistant, 理学部, 助手 (70183746)
ISHIMOTO Hiroyasu Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (90019472)
TOMARI Masataka Kanazawa University, Graduate School of Natural Science and Technology, Associat, 自然科学研究科, 助教授 (60183878)
KODAMA Akio Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (20111320)
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| Research Abstract |
Head investigator Fujimoto studied value-distribution-theoretic properties of meromorphic maps of C^n into P^N(C) and gave some new results as their applications.
He showed that, for 3N +1 hyperplanes H_j's in P^N(C) located in general position, there exists at most two meromorphic maps f of C^n into P^N(C) such that the inverse images f^<-1>(H_j)'s, which are counted with multiplicities truncated by two, coincide with given divisors D_j's. He also proved that, for 2N +2 hyperplanes H_j, in P^N(C) located in general position, there is some positive integer l_0 such that, if two meromorphic maps f and g of C^n into P_N(C) have the same inverse images counted with multiplicities truncated by l_0 for each H_j, then f and g are algebraically degenerate.
He also studied uniqueness range sets for meromorphic functions on C, namely, sets S with the property that the condition f^<-1>(S) = g^<-1>(S), counted f, g on C.For a finite set S = {a_1, a_2, ・・・, a_q}, he considers the polynomial P(w) : = (w - a_1)(w - a_2)・・・(w - a_q) and assumes that the derivative P(w) has k distinct zeros d_1, d_2, ・・・, d_h. He showed that, if k <greater than or equal> 4, q > 2k + 6, P(d_l) * P(d_m) for l * m and SIGMA_l P(d_l) * 0, then S is a uniqueness range set. He also gives some other sufficient conditions for a finite set to be a uniqueness range set.
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