{"product_id":"meromorphic-functions-over-non-archimedean-fields-pei-chu-hu-9780792365327","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).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Pei-Chu Hu,Chung-Chun Yang\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0792365321\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780792365327\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/30\/2000\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 295\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.34lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.75d\u003cbr\u003e\u003cbr\u003e\u003cb\u003eReview Citation(s): \u003c\/b\u003e\u003cbr\u003e\u003ci\u003eScitech Book News\u003c\/i\u003e 03\/01\/2001 pg. 40","brand":"Pei-Chu Hu","offers":[{"title":"Hardcover","offer_id":48992004112639,"sku":"9780792365327","price":54.99,"currency_code":"USD","in_stock":true}],"url":"https:\/\/www.whiterainbookhouse.com\/products\/meromorphic-functions-over-non-archimedean-fields-pei-chu-hu-9780792365327","provider":"WR Book House","version":"1.0","type":"link"}