{"product_id":"meromorphic-functions-over-non-archimedean-fields-von-chung-chun-yang-pei-chu-hu","title":"Meromorphic Functions over Non-Archimedean Fields","description":"Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two \"main theorems\" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k \u0026gt; 1; E. I. Nochka [99], [100],[101] for n \u0026gt; k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open).\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792365327\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048155460\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792365327","offer_id":50827672262,"sku":"9780792365327","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789048155460","offer_id":39415668605021,"sku":"9789048155460","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/36f38550-5f82-424c-9bc8-ab3bd4566e4b.jpg?v=1772088391","url":"https:\/\/shop.autorenwelt.de\/en\/products\/meromorphic-functions-over-non-archimedean-fields-von-chung-chun-yang-pei-chu-hu","provider":"Autorenwelt Shop","version":"1.0","type":"link"}