Theta Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1972
|
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
194 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by ("Sources" [9]). We shall restrict ourselves to postwar, i. e. , after 1945, periods. Around 1948/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I. A. S. (1948/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in "On the compactification of the Siegel space", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W. L. Baily in 1958 [1]. In 1957/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C. |
| Beschreibung: | 1 Online-Ressource (X, 234 p) |
| ISBN: | 9783642653155 9783642653179 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-65315-5 |
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Datensatz im Suchindex
| _version_ | 1804153097854910464 |
|---|---|
| any_adam_object | |
| author | Igusa, Jun-ichi |
| author_facet | Igusa, Jun-ichi |
| author_role | aut |
| author_sort | Igusa, Jun-ichi |
| author_variant | j i i jii |
| building | Verbundindex |
| bvnumber | BV042422866 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863800928 (DE-599)BVBBV042422866 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65315-5 |
| format | Electronic eBook |
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| id | DE-604.BV042422866 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642653155 9783642653179 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858283 |
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| physical | 1 Online-Ressource (X, 234 p) |
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| publishDate | 1972 |
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| series2 | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Igusa, Jun-ichi Verfasser aut Theta Functions by Jun-ichi Igusa Berlin, Heidelberg Springer Berlin Heidelberg 1972 1 Online-Ressource (X, 234 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 194 0072-7830 The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by ("Sources" [9]). We shall restrict ourselves to postwar, i. e. , after 1945, periods. Around 1948/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I. A. S. (1948/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in "On the compactification of the Siegel space", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W. L. Baily in 1958 [1]. In 1957/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C. Mathematics Mathematics, general Mathematik Thetafunktion (DE-588)4185175-4 gnd rswk-swf Thetafunktion (DE-588)4185175-4 s 1\p DE-604 https://doi.org/10.1007/978-3-642-65315-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Igusa, Jun-ichi Theta Functions Mathematics Mathematics, general Mathematik Thetafunktion (DE-588)4185175-4 gnd |
| subject_GND | (DE-588)4185175-4 |
| title | Theta Functions |
| title_auth | Theta Functions |
| title_exact_search | Theta Functions |
| title_full | Theta Functions by Jun-ichi Igusa |
| title_fullStr | Theta Functions by Jun-ichi Igusa |
| title_full_unstemmed | Theta Functions by Jun-ichi Igusa |
| title_short | Theta Functions |
| title_sort | theta functions |
| topic | Mathematics Mathematics, general Mathematik Thetafunktion (DE-588)4185175-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Thetafunktion |
| url | https://doi.org/10.1007/978-3-642-65315-5 |
| work_keys_str_mv | AT igusajunichi thetafunctions |