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Titlebook: Geometric and Analytic Number Theory; Edmund Hlawka,Rudolf Taschner,Johannes Schoi?engei Textbook 1991 Springer-Verlag Berlin Heidelberg 1

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書目名稱Geometric and Analytic Number Theory
編輯Edmund Hlawka,Rudolf Taschner,Johannes Schoi?engei
視頻videohttp://file.papertrans.cn/384/383633/383633.mp4
叢書名稱Universitext
圖書封面Titlebook: Geometric and Analytic Number Theory;  Edmund Hlawka,Rudolf Taschner,Johannes Schoi?engei Textbook 1991 Springer-Verlag Berlin Heidelberg 1
描述In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H. Lenstraj furthermore, tried and tested examples and exercises have been included. The translator, Prof. Charles Thomas, has solved the difficult problem of the German text into English in an admirable way. He deserves transferring our ‘Unreserved praise and special thailks. Finally, we would like to express our gratitude to Springer-Verlag, for their commitment to the publication of this English edition, and for the special care taken in its production. Vienna, March 1991 E. Hlawka J. SchoiBengeier R. Taschner Preface to the German Edition We have set ourselves two aims with the present book on number theory. On the one hand for a reader who has studied elementary number theory, and who has knowledge of analytic geometry, differential and integral calculus, together with the elements of complex variable theory, we wish to introduce basic results from the areas of the geometry of numbers, diophantine ap- proximation, prime number theory, and the asymptotic calculation of number theoretic functions. However on the other hand for the student who has al- ready studie
出版日期Textbook 1991
關(guān)鍵詞Diophantine approximation; Geometrie der Zahlen; Prime; Prime number; Primzahlverteilung; diophantische A
版次1
doihttps://doi.org/10.1007/978-3-642-75306-0
isbn_softcover978-3-540-52016-0
isbn_ebook978-3-642-75306-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag Berlin Heidelberg 1991
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https://doi.org/10.1007/978-3-642-79972-3rked out. Even simple questions about the way in which the number . + π is put together are unsolved up to now. Therefore the construction of real numbers from natural numbers is no simple problem. The theory of diophantine approximation seeks to understand how well, that is how closely, real numbers can be trapped by relations with the integers.
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The Kronecker Approximation Theorem,?. From the . point of view it involves rolling up the real line onto a circle of circumference 1, where the cle replaces the unit interval [0,1[. . open sets on the circle are identified as open sets on [0,1[, i.e. neighbourhoods in [0,1[ are defined by the quotient topology in ?/?. Considered in this way Dirichlet’s theorem states
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