Elliptic Curves: Diophantine Analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1978
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
231 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points |
| Beschreibung: | 1 Online-Ressource (XII, 264 p) |
| ISBN: | 9783662070109 9783642057175 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-07010-9 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423389 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1978 |||| o||u| ||||||eng d | ||
| 020 | |a 9783662070109 |c Online |9 978-3-662-07010-9 | ||
| 020 | |a 9783642057175 |c Print |9 978-3-642-05717-5 | ||
| 024 | 7 | |a 10.1007/978-3-662-07010-9 |2 doi | |
| 035 | |a (OCoLC)864104529 | ||
| 035 | |a (DE-599)BVBBV042423389 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Lang, Serge |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elliptic Curves |b Diophantine Analysis |c by Serge Lang |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1978 | |
| 300 | |a 1 Online-Ressource (XII, 264 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 231 |x 0072-7830 | |
| 500 | |a It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Elliptische Kurve |0 (DE-588)4014487-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diophantische Approximation |0 (DE-588)4135760-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diophantische Gleichung |0 (DE-588)4012386-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Kurve |0 (DE-588)4014487-2 |D s |
| 689 | 0 | 1 | |a Diophantische Gleichung |0 (DE-588)4012386-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Diophantische Approximation |0 (DE-588)4135760-7 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-662-07010-9 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858806 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153099084890112 |
|---|---|
| any_adam_object | |
| author | Lang, Serge |
| author_facet | Lang, Serge |
| author_role | aut |
| author_sort | Lang, Serge |
| author_variant | s l sl |
| building | Verbundindex |
| bvnumber | BV042423389 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864104529 (DE-599)BVBBV042423389 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-07010-9 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03073nmm a2200529zcb4500</leader><controlfield tag="001">BV042423389</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1978 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662070109</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-662-07010-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642057175</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-05717-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-662-07010-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)864104529</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423389</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lang, Serge</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elliptic Curves</subfield><subfield code="b">Diophantine Analysis</subfield><subfield code="c">by Serge Lang</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1978</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 264 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics</subfield><subfield code="v">231</subfield><subfield code="x">0072-7830</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Elliptische Kurve</subfield><subfield code="0">(DE-588)4014487-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diophantische Approximation</subfield><subfield code="0">(DE-588)4135760-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Diophantische Gleichung</subfield><subfield code="0">(DE-588)4012386-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Elliptische Kurve</subfield><subfield code="0">(DE-588)4014487-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Diophantische Gleichung</subfield><subfield code="0">(DE-588)4012386-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Diophantische Approximation</subfield><subfield code="0">(DE-588)4135760-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-662-07010-9</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858806</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042423389 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662070109 9783642057175 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858806 |
| oclc_num | 864104529 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 264 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Lang, Serge Verfasser aut Elliptic Curves Diophantine Analysis by Serge Lang Berlin, Heidelberg Springer Berlin Heidelberg 1978 1 Online-Ressource (XII, 264 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 231 0072-7830 It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points Mathematics Global analysis (Mathematics) Analysis Mathematik Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Diophantische Gleichung (DE-588)4012386-8 s 1\p DE-604 Diophantische Approximation (DE-588)4135760-7 s 2\p DE-604 https://doi.org/10.1007/978-3-662-07010-9 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 Elliptic Curves Diophantine Analysis Mathematics Global analysis (Mathematics) Analysis Mathematik Elliptische Kurve (DE-588)4014487-2 gnd Diophantische Approximation (DE-588)4135760-7 gnd Diophantische Gleichung (DE-588)4012386-8 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4135760-7 (DE-588)4012386-8 |
| title | Elliptic Curves Diophantine Analysis |
| title_auth | Elliptic Curves Diophantine Analysis |
| title_exact_search | Elliptic Curves Diophantine Analysis |
| title_full | Elliptic Curves Diophantine Analysis by Serge Lang |
| title_fullStr | Elliptic Curves Diophantine Analysis by Serge Lang |
| title_full_unstemmed | Elliptic Curves Diophantine Analysis by Serge Lang |
| title_short | Elliptic Curves |
| title_sort | elliptic curves diophantine analysis |
| title_sub | Diophantine Analysis |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Elliptische Kurve (DE-588)4014487-2 gnd Diophantische Approximation (DE-588)4135760-7 gnd Diophantische Gleichung (DE-588)4012386-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Elliptische Kurve Diophantische Approximation Diophantische Gleichung |
| url | https://doi.org/10.1007/978-3-662-07010-9 |
| work_keys_str_mv | AT langserge ellipticcurvesdiophantineanalysis |