Meromorphic Functions over Non-Archimedean Fields (Mathematics and Its Applications)

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9789048155460: Meromorphic Functions over Non-Archimedean Fields (Mathematics and Its Applications)
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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 > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open).

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9780792365327: Meromorphic Functions over Non-Archimedean Fields (Mathematics and Its Applications)

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ISBN 10:  0792365321 ISBN 13:  9780792365327
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Book Description Springer, Netherlands, 2010. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.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 > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman s conjecture partially solved by Hu-Yang [71J; Griffiths-Lang s conjecture (open). Softcover reprint of hardcover 1st ed. 2000. Seller Inventory # AAV9789048155460

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Book Description Springer, Netherlands, 2010. Paperback. Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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 > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman s conjecture partially solved by Hu-Yang [71J; Griffiths-Lang s conjecture (open). Softcover reprint of hardcover 1st ed. 2000. Seller Inventory # LIE9789048155460

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Book Description Springer, Netherlands, 2010. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****. 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 > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman s conjecture partially solved by Hu-Yang [71J; Griffiths-Lang s conjecture (open). Softcover reprint of hardcover 1st ed. 2000. Seller Inventory # AAV9789048155460

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Book Description Springer. Paperback. Condition: New. 295 pages. Dimensions: 9.0in. x 6.0in. x 0.7in.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 Shiffmans conjecture and Griffiths-Langs conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna98 for n k 1; H. Cartan 20 for n k 1; E. I. Nochka 99, 100, 101 for n k 1; Shiffmans conjecture partially solved by Hu-Yang 71J; Griffiths-Langs conjecture (open). This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Seller Inventory # 9789048155460

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