Download Meromorphic Functions over non-Archimedean Fields by Pei-Chu Hu,Chung-Chun Yang PDF

By Pei-Chu Hu,Chung-Chun Yang

Nevanlinna conception (or price distribution idea) in complicated research is so appealing that one may certainly have an interest in settling on how any such idea might glance within the non­ Archimedean research and Diophantine approximations. There are "main theorems" and disorder kinfolk that occupy a vital position in N evanlinna idea. They generate loads of purposes in learning strong point of meromorphic features, worldwide recommendations of differential equations, dynamics, etc. during this e-book, we'll introduce non-Archimedean analogues of Nevanlinna conception and its functions. In worth distribution concept, the most challenge is that given a holomorphic curve f : C -+ M right into a projective kind M of measurement n and a relations 01 of hypersurfaces on M, below a formal of non-degeneracy on f, locate the illness relation. If 01 n is a kinfolk of hyperplanes on M = r ordinarily place and if the smallest measurement of linear subspaces containing the picture f(C) is okay, Cartan conjectured that the sure of disorder relation is 2n - ok + 1. in general, if 01 is a kinfolk of admissible or basic crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. right here we checklist the method of this challenge: A. complicated research: (i) consistent pursuits: R. Nevanlinna[98] for n = ok = 1; H. Cartan [20] for n = ok > 1; E. I. Nochka [99], [100],[101] for n > ok ~ 1; Shiffman's conjecture partly solved by way of Hu-Yang [71J; Griffiths-Lang's conjecture (open).

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