Bounded gaps between primes: the epic breakthroughs of the early twenty-first century
Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite num...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
[2021]
|
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UPA01 Volltext |
| Zusammenfassung: | Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field |
| Beschreibung: | 1 Online-Ressource (xiv, 576 Seiten) |
| ISBN: | 9781108872201 |
| DOI: | 10.1017/9781108872201 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV047568632 | ||
| 003 | DE-604 | ||
| 005 | 20220929 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 211102s2021 |||| o||u| ||||||eng d | ||
| 020 | |a 9781108872201 |c Online |9 978-1-108-87220-1 | ||
| 024 | 7 | |a 10.1017/9781108872201 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781108872201 | ||
| 035 | |a (OCoLC)1284784583 | ||
| 035 | |a (DE-599)BVBBV047568632 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-739 |a DE-92 | ||
| 082 | 0 | |a 512.7/3 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 100 | 1 | |a Broughan, Kevin A. |d 1943- |e Verfasser |0 (DE-588)1137861630 |4 aut | |
| 245 | 1 | 0 | |a Bounded gaps between primes |b the epic breakthroughs of the early twenty-first century |c Kevin Broughan |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c [2021] | |
| 264 | 4 | |c © 2021 | |
| 300 | |a 1 Online-Ressource (xiv, 576 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 520 | |a Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field | ||
| 650 | 4 | |a Numbers, Prime | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Primzahltheorie |0 (DE-588)4175715-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | 1 | |a Primzahltheorie |0 (DE-588)4175715-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Hardcover |z 978-1-108-83674-6 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Paperback |z 978-1-108-79920-1 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/9781108872201 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032954300 | ||
| 966 | e | |u https://doi.org/10.1017/9781108872201 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781108872201 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781108872201 |l UPA01 |p ZDB-20-CBO |q UPA_PDA_CBO_Kauf2021 |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804182913368981504 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Broughan, Kevin A. 1943- |
| author_GND | (DE-588)1137861630 |
| author_facet | Broughan, Kevin A. 1943- |
| author_role | aut |
| author_sort | Broughan, Kevin A. 1943- |
| author_variant | k a b ka kab |
| building | Verbundindex |
| bvnumber | BV047568632 |
| classification_rvk | SK 180 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9781108872201 (OCoLC)1284784583 (DE-599)BVBBV047568632 |
| dewey-full | 512.7/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/3 |
| dewey-search | 512.7/3 |
| dewey-sort | 3512.7 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781108872201 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02959nmm a2200493zc 4500</leader><controlfield tag="001">BV047568632</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220929 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">211102s2021 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781108872201</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-108-87220-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/9781108872201</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781108872201</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1284784583</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV047568632</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-739</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7/3</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">Broughan, Kevin A.</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1137861630</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bounded gaps between primes</subfield><subfield code="b">the epic breakthroughs of the early twenty-first century</subfield><subfield code="c">Kevin Broughan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">[2021]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2021</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xiv, 576 Seiten)</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="520" ind1=" " ind2=" "><subfield code="a">Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numbers, Prime</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</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="650" ind1="0" ind2="7"><subfield code="a">Primzahltheorie</subfield><subfield code="0">(DE-588)4175715-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><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="1"><subfield code="a">Primzahltheorie</subfield><subfield code="0">(DE-588)4175715-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" 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">Druck-Ausgabe, Hardcover</subfield><subfield code="z">978-1-108-83674-6</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Paperback</subfield><subfield code="z">978-1-108-79920-1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/9781108872201</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:BVB01-032954300</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781108872201</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/10.1017/9781108872201</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><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781108872201</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UPA_PDA_CBO_Kauf2021</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV047568632 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:29:39Z |
| indexdate | 2024-07-10T09:15:06Z |
| institution | BVB |
| isbn | 9781108872201 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032954300 |
| oclc_num | 1284784583 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-92 |
| owner_facet | DE-12 DE-739 DE-92 |
| physical | 1 Online-Ressource (xiv, 576 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UPA_PDA_CBO_Kauf2021 |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Broughan, Kevin A. 1943- Verfasser (DE-588)1137861630 aut Bounded gaps between primes the epic breakthroughs of the early twenty-first century Kevin Broughan Cambridge Cambridge University Press [2021] © 2021 1 Online-Ressource (xiv, 576 Seiten) txt rdacontent c rdamedia cr rdacarrier Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field Numbers, Prime Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Primzahltheorie (DE-588)4175715-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Primzahltheorie (DE-588)4175715-4 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-1-108-83674-6 Erscheint auch als Druck-Ausgabe, Paperback 978-1-108-79920-1 https://doi.org/10.1017/9781108872201 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Broughan, Kevin A. 1943- Bounded gaps between primes the epic breakthroughs of the early twenty-first century Numbers, Prime Number theory Zahlentheorie (DE-588)4067277-3 gnd Primzahltheorie (DE-588)4175715-4 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4175715-4 |
| title | Bounded gaps between primes the epic breakthroughs of the early twenty-first century |
| title_auth | Bounded gaps between primes the epic breakthroughs of the early twenty-first century |
| title_exact_search | Bounded gaps between primes the epic breakthroughs of the early twenty-first century |
| title_exact_search_txtP | Bounded gaps between primes the epic breakthroughs of the early twenty-first century |
| title_full | Bounded gaps between primes the epic breakthroughs of the early twenty-first century Kevin Broughan |
| title_fullStr | Bounded gaps between primes the epic breakthroughs of the early twenty-first century Kevin Broughan |
| title_full_unstemmed | Bounded gaps between primes the epic breakthroughs of the early twenty-first century Kevin Broughan |
| title_short | Bounded gaps between primes |
| title_sort | bounded gaps between primes the epic breakthroughs of the early twenty first century |
| title_sub | the epic breakthroughs of the early twenty-first century |
| topic | Numbers, Prime Number theory Zahlentheorie (DE-588)4067277-3 gnd Primzahltheorie (DE-588)4175715-4 gnd |
| topic_facet | Numbers, Prime Number theory Zahlentheorie Primzahltheorie |
| url | https://doi.org/10.1017/9781108872201 |
| work_keys_str_mv | AT broughankevina boundedgapsbetweenprimestheepicbreakthroughsoftheearlytwentyfirstcentury |