| 書目名稱 | The Ball and Some Hilbert Problems | | 編輯 | Rolf-Peter Holzapfel | | 視頻video | http://file.papertrans.cn/905/904901/904901.mp4 | | 叢書名稱 | Lectures in Mathematics. ETH Zürich | | 圖書封面 |  | | 描述 | As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT‘S far-reaching program consisting of 23 prob- lems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field". This message can be found in the 12-th problem "Extension of KRONECKER‘S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS‘S pro- gram. It is dedicated to the construction of number fields | | 出版日期 | Book 1995 | | 關(guān)鍵詞 | Modular form; Schottky problem; Smooth function; differential equation; exponential function; minimum; mod | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-9051-9 | | isbn_softcover | 978-3-7643-2835-1 | | isbn_ebook | 978-3-0348-9051-9 | | copyright | Birkh?user Verlag 1995 |
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