Elliptic curves:
"This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses. An elliptic curve is a plane curve defi...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore
World Scientific
[2021]
|
| Ausgabe: | 2nd edition |
| Schlagworte: | |
| Zusammenfassung: | "This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses. An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer. Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work. The first three chapters develop the basic theory of elliptic curves. For this edition, the text has been completely revised and updated"-- |
| Beschreibung: | Literaturverzeichnis: Seite 297-304. - Index |
| Beschreibung: | x, 308 Seiten Diagramme |
| ISBN: | 9789811221835 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV047471722 | ||
| 003 | DE-604 | ||
| 005 | 20211115 | ||
| 007 | t | ||
| 008 | 210916s2021 xxu|||| |||| 00||| eng d | ||
| 020 | |a 9789811221835 |c Festeinband |9 978-981-12-2183-5 | ||
| 035 | |a (OCoLC)1195706000 | ||
| 035 | |a (DE-599)KXP1702007170 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c XD-US |a xxk |c XA-GB |a si |c XB-SG | ||
| 049 | |a DE-91G |a DE-83 | ||
| 050 | 0 | |a QA567.2.E44 | |
| 082 | 0 | |a 516.3/52 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 084 | |a 31.51 |2 bkl | ||
| 084 | |a MAT 145 |2 stub | ||
| 084 | |a 14H52 |2 msc | ||
| 100 | 1 | |a Milne, J. S. |d 1942- |0 (DE-588)1077746881 |4 aut | |
| 245 | 1 | 0 | |a Elliptic curves |c James S Milne ; University of Michigan, USA |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a New Jersey ; London ; Singapore |b World Scientific |c [2021] | |
| 300 | |a x, 308 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis: Seite 297-304. - Index | ||
| 520 | 3 | |a "This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses. An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer. Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work. The first three chapters develop the basic theory of elliptic curves. For this edition, the text has been completely revised and updated"-- | |
| 650 | 0 | 7 | |a Elliptische Kurve |0 (DE-588)4014487-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Curves, Elliptic | |
| 689 | 0 | 0 | |a Elliptische Kurve |0 (DE-588)4014487-2 |D s |
| 689 | 0 | 1 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Elliptische Kurve |0 (DE-588)4014487-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-981-122-184-2 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-981-122-185-9 |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032873372 | ||
Datensatz im Suchindex
| _version_ | 1804182783896059904 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Milne, J. S. 1942- |
| author_GND | (DE-588)1077746881 |
| author_facet | Milne, J. S. 1942- |
| author_role | aut |
| author_sort | Milne, J. S. 1942- |
| author_variant | j s m js jsm |
| building | Verbundindex |
| bvnumber | BV047471722 |
| callnumber-first | Q - Science |
| callnumber-label | QA567 |
| callnumber-raw | QA567.2.E44 |
| callnumber-search | QA567.2.E44 |
| callnumber-sort | QA 3567.2 E44 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 SK 240 |
| classification_tum | MAT 145 |
| ctrlnum | (OCoLC)1195706000 (DE-599)KXP1702007170 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2nd edition |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03205nam a2200505 c 4500</leader><controlfield tag="001">BV047471722</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20211115 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">210916s2021 xxu|||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789811221835</subfield><subfield code="c">Festeinband</subfield><subfield code="9">978-981-12-2183-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1195706000</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)KXP1702007170</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">XD-US</subfield><subfield code="a">xxk</subfield><subfield code="c">XA-GB</subfield><subfield code="a">si</subfield><subfield code="c">XB-SG</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA567.2.E44</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/52</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.51</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 145</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14H52</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Milne, J. S.</subfield><subfield code="d">1942-</subfield><subfield code="0">(DE-588)1077746881</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elliptic curves</subfield><subfield code="c">James S Milne ; University of Michigan, USA</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2nd edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New Jersey ; London ; Singapore</subfield><subfield code="b">World Scientific</subfield><subfield code="c">[2021]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">x, 308 Seiten</subfield><subfield code="b">Diagramme</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverzeichnis: Seite 297-304. - Index</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">"This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses. An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer. Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work. The first three chapters develop the basic theory of elliptic curves. For this edition, the text has been completely revised and updated"--</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">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Curves, Elliptic</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">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" 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="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-981-122-184-2</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-981-122-185-9</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-032873372</subfield></datafield></record></collection> |
| id | DE-604.BV047471722 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:09:34Z |
| indexdate | 2024-07-10T09:13:03Z |
| institution | BVB |
| isbn | 9789811221835 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032873372 |
| oclc_num | 1195706000 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-83 |
| physical | x, 308 Seiten Diagramme |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Milne, J. S. 1942- (DE-588)1077746881 aut Elliptic curves James S Milne ; University of Michigan, USA 2nd edition New Jersey ; London ; Singapore World Scientific [2021] x, 308 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seite 297-304. - Index "This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in first-year graduate courses. An elliptic curve is a plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated mathematicians since ancient times, it was not until 1922 that Mordell proved that the points form a finitely generated group. There is still no proven algorithm for finding the rank of the group, but in one of the earliest important applications of computers to mathematics, Birch and Swinnerton-Dyer discovered a relation between the rank and the numbers of points on the curve computed modulo a prime. Chapter IV of the book proves Mordell's theorem and explains the conjecture of Birch and Swinnerton-Dyer. Every elliptic curve over the rational numbers has an L-series attached to it.Hasse conjectured that this L-series satisfies a functional equation, and in 1955 Taniyama suggested that Hasse's conjecture could be proved by showing that the L-series arises from a modular form. This was shown to be correct by Wiles (and others) in the 1990s, and, as a consequence, one obtains a proof of Fermat's Last Theorem. Chapter V of the book is devoted to explaining this work. The first three chapters develop the basic theory of elliptic curves. For this edition, the text has been completely revised and updated"-- Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Curves, Elliptic Elliptische Kurve (DE-588)4014487-2 s Zahlentheorie (DE-588)4067277-3 s DE-604 Erscheint auch als Online-Ausgabe 978-981-122-184-2 Erscheint auch als Online-Ausgabe 978-981-122-185-9 |
| spellingShingle | Milne, J. S. 1942- Elliptic curves Elliptische Kurve (DE-588)4014487-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4067277-3 |
| title | Elliptic curves |
| title_auth | Elliptic curves |
| title_exact_search | Elliptic curves |
| title_exact_search_txtP | Elliptic curves |
| title_full | Elliptic curves James S Milne ; University of Michigan, USA |
| title_fullStr | Elliptic curves James S Milne ; University of Michigan, USA |
| title_full_unstemmed | Elliptic curves James S Milne ; University of Michigan, USA |
| title_short | Elliptic curves |
| title_sort | elliptic curves |
| topic | Elliptische Kurve (DE-588)4014487-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Elliptische Kurve Zahlentheorie |
| work_keys_str_mv | AT milnejs ellipticcurves |