| 書目名稱 | Elliptic Modular Functions | | 副標題 | An Introduction | | 編輯 | Bruno Schoeneberg | | 視頻video | http://file.papertrans.cn/308/307798/307798.mp4 | | 叢書名稱 | Grundlehren der mathematischen Wissenschaften | | 圖書封面 |  | | 描述 | This book is a fully detailed introduction to the theory of modular functions of a single variable. I hope that it will fill gaps which in view ofthe lively development ofthis theory have often been an obstacle to the students‘ progress. The study of the book requires an elementary knowledge of algebra, number theory and topology and a deeper knowledge of the theory of functions. An extensive discussion of the modular group SL(2, Z) is followed by the introduction to the theory of automorphic functions and auto- morphic forms of integral dimensions belonging to SL(2,Z). The theory is developed first via the Riemann mapping theorem and then again with the help of Eisenstein series. An investigation of the subgroups of SL(2, Z) and the introduction of automorphic functions and forms belonging to these groups folIows. Special attention is given to the subgroups of finite index in SL (2, Z) and, among these, to the so-called congruence groups. The decisive role in this setting is assumed by the Riemann-Roch theorem. Since its proof may be found in the literature, only the pertinent basic concepts are outlined. For the extension of the theory, special fields of modular functions- in par | | 出版日期 | Book 1974 | | 關(guān)鍵詞 | Elliptische Modulfunktion; Finite; Functions; Modular form; congruence; construction; convergence; developm | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-65663-7 | | isbn_softcover | 978-3-642-65665-1 | | isbn_ebook | 978-3-642-65663-7Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin Heidelberg 1974 |
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