The Erdős distance problem:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2011]
|
| Schriftenreihe: | Student mathematical library
volume 56 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021130014&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xii, 150 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821852811 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV037216023 | ||
| 003 | DE-604 | ||
| 005 | 20230323 | ||
| 007 | t| | ||
| 008 | 110209s2011 xx a||| |||| 00||| eng d | ||
| 020 | |a 9780821852811 |c pbk. |9 978-0-8218-5281-1 | ||
| 035 | |a (OCoLC)657223794 | ||
| 035 | |a (DE-599)BVBBV037216023 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-188 |a DE-20 |a DE-384 |a DE-703 |a DE-824 |a DE-19 |a DE-11 | ||
| 082 | 0 | |a 511/.6 |2 22 | |
| 084 | |a SK 170 |0 (DE-625)143221: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a 05B30 |2 msc | ||
| 100 | 1 | |a Garibaldi, Julia |d 1976- |e Verfasser |0 (DE-588)1029542511 |4 aut | |
| 245 | 1 | 0 | |a The Erdős distance problem |c Julia Garibaldi ; Alex Iosevich ; Steven Senger |
| 246 | 1 | 3 | |a The Erdös distance problem |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2011] | |
| 264 | 4 | |c © 2011 | |
| 300 | |a xii, 150 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v volume 56 | |
| 650 | 0 | 7 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kombinatorik |0 (DE-588)4031824-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |D s |
| 689 | 0 | 1 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | 2 | |a Kombinatorik |0 (DE-588)4031824-2 |D s |
| 689 | 0 | 3 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Iosevich, Alex |d 1967- |e Verfasser |0 (DE-588)143424815 |4 aut | |
| 700 | 1 | |a Senger, Steven |d 1982- |e Verfasser |0 (DE-588)1029542651 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1639-3 |
| 830 | 0 | |a Student mathematical library |v volume 56 |w (DE-604)BV013184751 |9 56 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021130014&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-021130014 | |
Datensatz im Suchindex
| _version_ | 1819247931005337600 |
|---|---|
| adam_text | Contents
Foreword
ix
Acknowledgements
xi
Introduction
1
§1.
A sketch of our problem
1
§2.
Some notation
3
Exercises
5
Chapter
1.
The -Jn theory
7
§1.
Erdős
original argument
7
§2.
Higher dimensions
9
§3.
Arbitrary metrics
11
Exercises
13
Chapter
2.
The
п2/3
theory
15
§1.
The
Erdős
integer distance principle
15
§2. Mosers
construction
16
Exercises
20
Chapter
3.
The Cauchy-Schwarz inequality
23
§1.
Proof of the Cauchy-Schwarz inequality
23
vi
Contents
§2.
Application:
Projections
25
Chapter
4.
Graph theory and incidences
29
§1.
Basic graph theory
29
§2.
Crossing numbers
33
§3.
Incidence matrices and Cauchy-Schwarz
36
§4.
The
Szemerédi-
Trotter incidence theorem
38
Exercises
42
Chapter
5.
The n4/5 theory
45
§1.
The Euclidean case: Straight line bisectors
45
§2.
Convexity and potatoes
51
§3.
Székely s
method for potato metrics
56
Exercises
61
Chapter
6.
The n6/7 theory
65
§1.
The setup
65
§2.
Arithmetic enters the picture
67
Exercises
69
Chapter
7.
Beyond n6/7 71
§1.
Sums and entries
71
§2.
Tardos
elementary argument
72
§3.
Katz-Tardos method 74
§4.
Ruzsa s construction
77
Chapter
8.
Information theory
81
§1.
What is this information of which you speak?
81
§2.
More information never hurts
83
§3.
Application to the sums and entries problem
88
Chapter
9.
Dot products 91
§1.
Transferring ideas
§2.
Székely s
method 93
§3.
Special cases
Contents
vii
Exercises
99
Chapter
10.
Vector spaces over finite fields
101
§1.
Finite fields
101
§2.
Vector spaces
103
§3.
Exponential sums in finite fields
109
§4.
The Fourier transform
115
Chapter
11.
Distances in vector spaces over finite fields
119
§1.
The setup
119
§2.
The argument
121
Chapter
12.
Applications of the
Erdős
distance problem
127
Appendix A. Hyperbolas in the plane
131
Appendix B. Basic probability theory
135
Appendix
С
Jensen s inequality
139
Bibliography
143
Biographical information
147
Index
149
|
| any_adam_object | 1 |
| author | Garibaldi, Julia 1976- Iosevich, Alex 1967- Senger, Steven 1982- |
| author_GND | (DE-588)1029542511 (DE-588)143424815 (DE-588)1029542651 |
| author_facet | Garibaldi, Julia 1976- Iosevich, Alex 1967- Senger, Steven 1982- |
| author_role | aut aut aut |
| author_sort | Garibaldi, Julia 1976- |
| author_variant | j g jg a i ai s s ss |
| building | Verbundindex |
| bvnumber | BV037216023 |
| classification_rvk | SK 170 SK 180 |
| ctrlnum | (OCoLC)657223794 (DE-599)BVBBV037216023 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.6 |
| dewey-search | 511/.6 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02220nam a2200505 cb4500</leader><controlfield tag="001">BV037216023</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230323 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">110209s2011 xx a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821852811</subfield><subfield code="c">pbk.</subfield><subfield code="9">978-0-8218-5281-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)657223794</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV037216023</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-83</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511/.6</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 170</subfield><subfield code="0">(DE-625)143221:</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="084" ind1=" " ind2=" "><subfield code="a">05B30</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Garibaldi, Julia</subfield><subfield code="d">1976-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1029542511</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Erdős distance problem</subfield><subfield code="c">Julia Garibaldi ; Alex Iosevich ; Steven Senger</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">The Erdös distance problem</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">[2011]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xii, 150 Seiten</subfield><subfield code="b">Illustrationen, 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="490" ind1="1" ind2=" "><subfield code="a">Student mathematical library</subfield><subfield code="v">volume 56</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorische Analysis</subfield><subfield code="0">(DE-588)4164746-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorik</subfield><subfield code="0">(DE-588)4031824-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</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="689" ind1="0" ind2="0"><subfield code="a">Kombinatorische Analysis</subfield><subfield code="0">(DE-588)4164746-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Kombinatorik</subfield><subfield code="0">(DE-588)4031824-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><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="700" ind1="1" ind2=" "><subfield code="a">Iosevich, Alex</subfield><subfield code="d">1967-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)143424815</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Senger, Steven</subfield><subfield code="d">1982-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1029542651</subfield><subfield code="4">aut</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">978-1-4704-1639-3</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Student mathematical library</subfield><subfield code="v">volume 56</subfield><subfield code="w">(DE-604)BV013184751</subfield><subfield code="9">56</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021130014&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-021130014</subfield></datafield></record></collection> |
| id | DE-604.BV037216023 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:46:51Z |
| institution | BVB |
| isbn | 9780821852811 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021130014 |
| oclc_num | 657223794 |
| open_access_boolean | |
| owner | DE-83 DE-188 DE-20 DE-384 DE-703 DE-824 DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-83 DE-188 DE-20 DE-384 DE-703 DE-824 DE-19 DE-BY-UBM DE-11 |
| physical | xii, 150 Seiten Illustrationen, Diagramme |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spellingShingle | Garibaldi, Julia 1976- Iosevich, Alex 1967- Senger, Steven 1982- The Erdős distance problem Student mathematical library Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd Harmonische Analyse (DE-588)4023453-8 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4031824-2 (DE-588)4023453-8 (DE-588)4067277-3 |
| title | The Erdős distance problem |
| title_alt | The Erdös distance problem |
| title_auth | The Erdős distance problem |
| title_exact_search | The Erdős distance problem |
| title_full | The Erdős distance problem Julia Garibaldi ; Alex Iosevich ; Steven Senger |
| title_fullStr | The Erdős distance problem Julia Garibaldi ; Alex Iosevich ; Steven Senger |
| title_full_unstemmed | The Erdős distance problem Julia Garibaldi ; Alex Iosevich ; Steven Senger |
| title_short | The Erdős distance problem |
| title_sort | the erdos distance problem |
| topic | Kombinatorische Analysis (DE-588)4164746-4 gnd Kombinatorik (DE-588)4031824-2 gnd Harmonische Analyse (DE-588)4023453-8 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Kombinatorische Analysis Kombinatorik Harmonische Analyse Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021130014&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184751 |
| work_keys_str_mv | AT garibaldijulia theerdosdistanceproblem AT iosevichalex theerdosdistanceproblem AT sengersteven theerdosdistanceproblem |