Abelian Varieties with Complex Multiplication and Modular Functions:
Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular funct...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Princeton, NJ
Princeton University Press
[2016]
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| Schriftenreihe: | Princeton mathematical series
46 |
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| Online-Zugang: | Volltext |
| Zusammenfassung: | Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Oct. 27, 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400883943 |
| DOI: | 10.1515/9781400883943 |
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| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Oct. 27, 2016) | ||
| 520 | |a Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively | ||
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Datensatz im Suchindex
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| author | Shimura, Goro 1930-2019 |
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| author_facet | Shimura, Goro 1930-2019 |
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| author_sort | Shimura, Goro 1930-2019 |
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| bvnumber | BV043979319 |
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| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400883943 |
| format | Electronic eBook |
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| spelling | Shimura, Goro 1930-2019 Verfasser (DE-588)12425067X aut Abelian Varieties with Complex Multiplication and Modular Functions Goro Shimura Princeton, NJ Princeton University Press [2016] © 1998 1 online resource txt rdacontent c rdamedia cr rdacarrier Princeton mathematical series 46 Description based on online resource; title from PDF title page (publisher's Web site, viewed Oct. 27, 2016) Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively In English Abelian varieties Modular functions Modulfunktion (DE-588)4039855-9 gnd rswk-swf Komplexe Multiplikation (DE-588)4164903-5 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Komplexe Multiplikation (DE-588)4164903-5 s Modulfunktion (DE-588)4039855-9 s DE-604 Erscheint auch als Druck-Ausgabe 0-691-01656-9 Princeton mathematical series 46 (DE-604)BV045898993 46 https://doi.org/10.1515/9781400883943?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Shimura, Goro 1930-2019 Abelian Varieties with Complex Multiplication and Modular Functions Princeton mathematical series Abelian varieties Modular functions Modulfunktion (DE-588)4039855-9 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd |
| subject_GND | (DE-588)4039855-9 (DE-588)4164903-5 (DE-588)4140992-9 |
| title | Abelian Varieties with Complex Multiplication and Modular Functions |
| title_auth | Abelian Varieties with Complex Multiplication and Modular Functions |
| title_exact_search | Abelian Varieties with Complex Multiplication and Modular Functions |
| title_full | Abelian Varieties with Complex Multiplication and Modular Functions Goro Shimura |
| title_fullStr | Abelian Varieties with Complex Multiplication and Modular Functions Goro Shimura |
| title_full_unstemmed | Abelian Varieties with Complex Multiplication and Modular Functions Goro Shimura |
| title_short | Abelian Varieties with Complex Multiplication and Modular Functions |
| title_sort | abelian varieties with complex multiplication and modular functions |
| topic | Abelian varieties Modular functions Modulfunktion (DE-588)4039855-9 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd |
| topic_facet | Abelian varieties Modular functions Modulfunktion Komplexe Multiplikation Abelsche Mannigfaltigkeit |
| url | https://doi.org/10.1515/9781400883943?locatt=mode:legacy |
| volume_link | (DE-604)BV045898993 |
| work_keys_str_mv | AT shimuragoro abelianvarietieswithcomplexmultiplicationandmodularfunctions |