Diophantine equations over function fields:
Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been mad...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1984
|
| Schriftenreihe: | London Mathematical Society lecture note series
96 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 125 pages) |
| ISBN: | 9780511752490 |
| DOI: | 10.1017/CBO9780511752490 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043942168 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s1984 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511752490 |c Online |9 978-0-511-75249-0 | ||
| 024 | 7 | |a 10.1017/CBO9780511752490 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511752490 | ||
| 035 | |a (OCoLC)967776280 | ||
| 035 | |a (DE-599)BVBBV043942168 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 512/.74 |2 19eng | |
| 084 | |a SI 320 |0 (DE-625)143123: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 100 | 1 | |a Mason, R. C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Diophantine equations over function fields |c R.C. Mason |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1984 | |
| 300 | |a 1 online resource (x, 125 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a London Mathematical Society lecture note series |v 96 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate | ||
| 650 | 4 | |a Diophantine equations | |
| 650 | 4 | |a Algebraic fields | |
| 650 | 0 | 7 | |a Funktionenkörper |0 (DE-588)4155688-4 |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 Diophantische Gleichung |0 (DE-588)4012386-8 |D s |
| 689 | 0 | 1 | |a Funktionenkörper |0 (DE-588)4155688-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-26983-4 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511752490 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029351137 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511752490 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511752490 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176884686127104 |
|---|---|
| any_adam_object | |
| author | Mason, R. C. |
| author_facet | Mason, R. C. |
| author_role | aut |
| author_sort | Mason, R. C. |
| author_variant | r c m rc rcm |
| building | Verbundindex |
| bvnumber | BV043942168 |
| classification_rvk | SI 320 SK 180 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511752490 (OCoLC)967776280 (DE-599)BVBBV043942168 |
| dewey-full | 512/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.74 |
| dewey-search | 512/.74 |
| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511752490 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03692nmm a2200505zcb4500</leader><controlfield tag="001">BV043942168</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s1984 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511752490</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-75249-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511752490</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511752490</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)967776280</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043942168</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-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.74</subfield><subfield code="2">19eng</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="0">(DE-625)143123:</subfield><subfield code="2">rvk</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="100" ind1="1" ind2=" "><subfield code="a">Mason, R. C.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Diophantine equations over function fields</subfield><subfield code="c">R.C. Mason</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">1984</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (x, 125 pages)</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">London Mathematical Society lecture note series</subfield><subfield code="v">96</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Diophantine equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic fields</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionenkörper</subfield><subfield code="0">(DE-588)4155688-4</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">Diophantische Gleichung</subfield><subfield code="0">(DE-588)4012386-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Funktionenkörper</subfield><subfield code="0">(DE-588)4155688-4</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="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-26983-4</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511752490</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-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029351137</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="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511752490</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511752490</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043942168 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511752490 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351137 |
| oclc_num | 967776280 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 125 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Mason, R. C. Verfasser aut Diophantine equations over function fields R.C. Mason Cambridge Cambridge University Press 1984 1 online resource (x, 125 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 96 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate Diophantine equations Algebraic fields Funktionenkörper (DE-588)4155688-4 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 s Funktionenkörper (DE-588)4155688-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-26983-4 https://doi.org/10.1017/CBO9780511752490 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mason, R. C. Diophantine equations over function fields Diophantine equations Algebraic fields Funktionenkörper (DE-588)4155688-4 gnd Diophantische Gleichung (DE-588)4012386-8 gnd |
| subject_GND | (DE-588)4155688-4 (DE-588)4012386-8 |
| title | Diophantine equations over function fields |
| title_auth | Diophantine equations over function fields |
| title_exact_search | Diophantine equations over function fields |
| title_full | Diophantine equations over function fields R.C. Mason |
| title_fullStr | Diophantine equations over function fields R.C. Mason |
| title_full_unstemmed | Diophantine equations over function fields R.C. Mason |
| title_short | Diophantine equations over function fields |
| title_sort | diophantine equations over function fields |
| topic | Diophantine equations Algebraic fields Funktionenkörper (DE-588)4155688-4 gnd Diophantische Gleichung (DE-588)4012386-8 gnd |
| topic_facet | Diophantine equations Algebraic fields Funktionenkörper Diophantische Gleichung |
| url | https://doi.org/10.1017/CBO9780511752490 |
| work_keys_str_mv | AT masonrc diophantineequationsoverfunctionfields |