Algebraic Number Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1994
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Graduate Texts in Mathematics
110 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which I make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collection of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of Weber, Hasse, Hecke, and Hilbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theoretically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre's book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, I have intermingled the ideal and idelic approaches without prejudice for either. I also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods) |
| Beschreibung: | 1 Online-Ressource (XIII, 357 p) |
| ISBN: | 9781461208532 9781461269229 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-0853-2 |
Internformat
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Datensatz im Suchindex
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| author | Lang, Serge 1927-2005 |
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| author_facet | Lang, Serge 1927-2005 |
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| author_sort | Lang, Serge 1927-2005 |
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0853-2 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042419648 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461208532 9781461269229 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855065 |
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| physical | 1 Online-Ressource (XIII, 357 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer New York |
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| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Algebraic Number Theory by Serge Lang Second Edition New York, NY Springer New York 1994 1 Online-Ressource (XIII, 357 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 110 0072-5285 The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which I make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collection of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of Weber, Hasse, Hecke, and Hilbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theoretically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre's book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, I have intermingled the ideal and idelic approaches without prejudice for either. I also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods) Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s 1\p DE-604 Analytische Zahlentheorie (DE-588)4001870-2 s 2\p DE-604 Graduate Texts in Mathematics 110 (DE-604)BV035421258 110 https://doi.org/10.1007/978-1-4612-0853-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge 1927-2005 Algebraic Number Theory Graduate Texts in Mathematics Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4001870-2 (DE-588)4001170-7 |
| title | Algebraic Number Theory |
| title_auth | Algebraic Number Theory |
| title_exact_search | Algebraic Number Theory |
| title_full | Algebraic Number Theory by Serge Lang |
| title_fullStr | Algebraic Number Theory by Serge Lang |
| title_full_unstemmed | Algebraic Number Theory by Serge Lang |
| title_short | Algebraic Number Theory |
| title_sort | algebraic number theory |
| topic | Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie Algebraische Zahlentheorie |
| url | https://doi.org/10.1007/978-1-4612-0853-2 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT langserge algebraicnumbertheory |