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Titlebook: Introduction to Complex Hyperbolic Spaces; Serge Lang Book 1987 Springer Science+Business Media New York 1987 Diophantine approximation.Fi

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發(fā)表于 2025-3-21 19:48:24 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Introduction to Complex Hyperbolic Spaces
編輯Serge Lang
視頻videohttp://file.papertrans.cn/474/473539/473539.mp4
圖書封面Titlebook: Introduction to Complex Hyperbolic Spaces;  Serge Lang Book 1987 Springer Science+Business Media New York 1987 Diophantine approximation.Fi
描述Since the appearance of Kobayashi‘s book, there have been several re- sults at the basic level of hyperbolic spaces, for instance Brody‘s theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re- produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super- sede Kobayashi‘s. My interest in these matters stems from their relations with diophan- tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan- linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case a
出版日期Book 1987
關鍵詞Diophantine approximation; Finite; Nevanlinna theory; approximation; boundary element method; complex num
版次1
doihttps://doi.org/10.1007/978-1-4757-1945-1
isbn_softcover978-1-4419-3082-8
isbn_ebook978-1-4757-1945-1
copyrightSpringer Science+Business Media New York 1987
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沙發(fā)
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板凳
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Basic Properties,rem for families of such maps. Such an application has wide ramifications, including possible applications to problems associated with Mordell’s conjecture (Faltings’ theorem) and possible generalizations.
地板
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https://doi.org/10.1007/978-1-4757-1945-1Diophantine approximation; Finite; Nevanlinna theory; approximation; boundary element method; complex num
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Hyperbolic Imbeddings,This chapter and the next chapter on Brody’s theorem are essentially logically independent. The reader interested in Brody’s theorem should skip this chapter at first, and come back to it only as needed to get the extra information that under certain circumstances imbeddings are hyperbolic.
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Nevanlinna Theory,In classical estimates of orders of growth of an entire function, one uses the measure of growth given by
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Applications to Holomorphic Curves in ,,,In this chapter we start with Borel’s theorem of 1897, concerning linear relations between entire functions without zeros. Its proof depends only on a very easy and brief application of Jensen’s formula via Lemmas 3.2 and 3.7, and could consequently be done in standard basic courses in complex variables.
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