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In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the $p$-Casorati determinant with $p\in\mathbb C^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition ``order=0". The results obtained include $p$-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.
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참고문헌 (19)
참고문헌 신청
D. C. Barnett / 2007 / Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations / Proc. Roy. Soc. Edinburgh Sect. A 137(3):457~474
T. B. Cao / 2014 / Difference analogues of the second main theorem for meromorphic functions in several complex variables / Math. Nachr. 287(5-6):530~545
T. B. Cao / 2016 / A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables / J. Math. Anal. Appl. 444(2):1114~1132
H. Cartan / 1933 / Sur les zeros des combinaisons lineaires de pfonctions holomorphes donnees / Mathematica Cluj 7:531
H. Fujimoto / 1975 / The uniqueness problem of meromorphic maps into the complex projective space / Nagoya Math. J. 58:1~23
T. B. Cao / 2014 / Difference analogues of the second main theorem for meromorphic functions in several complex variables / Math. Nachr. 287(5-6):530~545
T. B. Cao / 2016 / A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables / J. Math. Anal. Appl. 444(2):1114~1132
H. Cartan / 1933 / Sur les zeros des combinaisons lineaires de pfonctions holomorphes donnees / Mathematica Cluj 7:531
H. Fujimoto / 1975 / The uniqueness problem of meromorphic maps into the complex projective space / Nagoya Math. J. 58:1~23
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