Elliptic Curves. (MN-40), Volume 40:
An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together i...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1993]
|
| Schriftenreihe: | Mathematical Notes
40 |
| Schlagworte: | |
| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-859 DE-860 DE-739 Volltext |
| Zusammenfassung: | An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9780691186900 |
| DOI: | 10.1515/9780691186900 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV047666733 | ||
| 003 | DE-604 | ||
| 005 | 20221115 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 220112s1993 xx o|||| 00||| eng d | ||
| 020 | |a 9780691186900 |9 978-0-691-18690-0 | ||
| 024 | 7 | |a 10.1515/9780691186900 |2 doi | |
| 035 | |a (ZDB-23-DGG)9780691186900 | ||
| 035 | |a (OCoLC)1101919676 | ||
| 035 | |a (DE-599)BVBBV047666733 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1043 |a DE-858 |a DE-859 |a DE-860 |a DE-739 | ||
| 082 | 0 | |a 516.3/52 |2 23 | |
| 100 | 1 | |a Knapp, Anthony W. |d 1941- |e Verfasser |0 (DE-588)132959690 |4 aut | |
| 245 | 1 | 0 | |a Elliptic Curves. (MN-40), Volume 40 |c Anthony W. Knapp |
| 264 | 1 | |a Princeton, NJ |b Princeton University Press |c [1993] | |
| 264 | 4 | |c © 1993 | |
| 300 | |a 1 Online-Ressource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematical Notes |v 40 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) | ||
| 520 | |a An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner | ||
| 546 | |a In English | ||
| 650 | 7 | |a MATHEMATICS / Geometry / Algebraic |2 bisacsh | |
| 650 | 4 | |a Curves, Elliptic | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9780691186900?locatt=mode:legacy |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-23-DGG | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-033051454 | |
| 966 | e | |u https://doi.org/10.1515/9780691186900?locatt=mode:legacy |l DE-1043 |p ZDB-23-DGG |q FAB_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9780691186900?locatt=mode:legacy |l DE-1046 |p ZDB-23-DGG |q FAW_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9780691186900?locatt=mode:legacy |l DE-858 |p ZDB-23-DGG |q FCO_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9780691186900?locatt=mode:legacy |l DE-859 |p ZDB-23-DGG |q FKE_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9780691186900?locatt=mode:legacy |l DE-860 |p ZDB-23-DGG |q FLA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9780691186900?locatt=mode:legacy |l DE-739 |p ZDB-23-DGG |q UPA_PDA_DGG |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1824507916852396032 |
|---|---|
| adam_text | |
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Knapp, Anthony W. 1941- |
| author_GND | (DE-588)132959690 |
| author_facet | Knapp, Anthony W. 1941- |
| author_role | aut |
| author_sort | Knapp, Anthony W. 1941- |
| author_variant | a w k aw awk |
| building | Verbundindex |
| bvnumber | BV047666733 |
| collection | ZDB-23-DGG |
| ctrlnum | (ZDB-23-DGG)9780691186900 (OCoLC)1101919676 (DE-599)BVBBV047666733 |
| 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 |
| doi_str_mv | 10.1515/9780691186900 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zcb4500</leader><controlfield tag="001">BV047666733</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20221115</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">220112s1993 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780691186900</subfield><subfield code="9">978-0-691-18690-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9780691186900</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-23-DGG)9780691186900</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1101919676</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV047666733</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="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1043</subfield><subfield code="a">DE-858</subfield><subfield code="a">DE-859</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-739</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/52</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Knapp, Anthony W.</subfield><subfield code="d">1941-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)132959690</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elliptic Curves. (MN-40), Volume 40</subfield><subfield code="c">Anthony W. Knapp</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">[1993]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource</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">Mathematical Notes</subfield><subfield code="v">40</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Geometry / Algebraic</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Curves, Elliptic</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9780691186900?locatt=mode:legacy</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-033051454</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9780691186900?locatt=mode:legacy</subfield><subfield code="l">DE-1043</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAB_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9780691186900?locatt=mode:legacy</subfield><subfield code="l">DE-1046</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAW_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9780691186900?locatt=mode:legacy</subfield><subfield code="l">DE-858</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FCO_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9780691186900?locatt=mode:legacy</subfield><subfield code="l">DE-859</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FKE_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9780691186900?locatt=mode:legacy</subfield><subfield code="l">DE-860</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FLA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9780691186900?locatt=mode:legacy</subfield><subfield code="l">DE-739</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UPA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV047666733 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:54:14Z |
| indexdate | 2025-02-19T17:32:20Z |
| institution | BVB |
| isbn | 9780691186900 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033051454 |
| oclc_num | 1101919676 |
| open_access_boolean | |
| owner | DE-1046 DE-1043 DE-858 DE-859 DE-860 DE-739 |
| owner_facet | DE-1046 DE-1043 DE-858 DE-859 DE-860 DE-739 |
| physical | 1 Online-Ressource |
| psigel | ZDB-23-DGG ZDB-23-DGG FAB_PDA_DGG ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FCO_PDA_DGG ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DGG UPA_PDA_DGG |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Princeton University Press |
| record_format | marc |
| series2 | Mathematical Notes |
| spelling | Knapp, Anthony W. 1941- Verfasser (DE-588)132959690 aut Elliptic Curves. (MN-40), Volume 40 Anthony W. Knapp Princeton, NJ Princeton University Press [1993] © 1993 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Mathematical Notes 40 Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner In English MATHEMATICS / Geometry / Algebraic bisacsh Curves, Elliptic https://doi.org/10.1515/9780691186900?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Knapp, Anthony W. 1941- Elliptic Curves. (MN-40), Volume 40 MATHEMATICS / Geometry / Algebraic bisacsh Curves, Elliptic |
| title | Elliptic Curves. (MN-40), Volume 40 |
| title_auth | Elliptic Curves. (MN-40), Volume 40 |
| title_exact_search | Elliptic Curves. (MN-40), Volume 40 |
| title_exact_search_txtP | Elliptic Curves. (MN-40), Volume 40 |
| title_full | Elliptic Curves. (MN-40), Volume 40 Anthony W. Knapp |
| title_fullStr | Elliptic Curves. (MN-40), Volume 40 Anthony W. Knapp |
| title_full_unstemmed | Elliptic Curves. (MN-40), Volume 40 Anthony W. Knapp |
| title_short | Elliptic Curves. (MN-40), Volume 40 |
| title_sort | elliptic curves mn 40 volume 40 |
| topic | MATHEMATICS / Geometry / Algebraic bisacsh Curves, Elliptic |
| topic_facet | MATHEMATICS / Geometry / Algebraic Curves, Elliptic |
| url | https://doi.org/10.1515/9780691186900?locatt=mode:legacy |
| work_keys_str_mv | AT knappanthonyw ellipticcurvesmn40volume40 |