{"product_id":"meromorphic-functions-over-non-archimedean-fields-9789048155460","title":"Meromorphic Functions Over Non-Archimedean Fields","description":"\u003cp\u003e • Author(s): Pei-Chu Hu\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eNevanlinna 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).\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45282456109207,"sku":"9789048155460","price":3639.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9789048155460.webp?v=1769302200","url":"https:\/\/atlanticbooks.com\/products\/meromorphic-functions-over-non-archimedean-fields-9789048155460","provider":"Atlantic Books","version":"1.0","type":"link"}