The prime number theorem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society student texts
53 |
| Schlagworte: | |
| Online-Zugang: | Table of contents Publisher description Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 252 S. |
| ISBN: | 0521814111 0521891108 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV014630034 | ||
| 003 | DE-604 | ||
| 005 | 20150205 | ||
| 007 | t | ||
| 008 | 020731s2003 xxk |||| 00||| eng d | ||
| 010 | |a 2002074199 | ||
| 020 | |a 0521814111 |9 0-521-81411-1 | ||
| 020 | |a 0521891108 |9 0-521-89110-8 | ||
| 035 | |a (OCoLC)50253282 | ||
| 035 | |a (DE-599)BVBBV014630034 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxk |c GB | ||
| 049 | |a DE-355 |a DE-29T |a DE-91G |a DE-19 |a DE-11 |a DE-188 |a DE-384 | ||
| 050 | 0 | |a QA246 | |
| 082 | 0 | |a 512/.72 |2 21 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a MAT 100f |2 stub | ||
| 100 | 1 | |a Jameson, Graham J. O. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The prime number theorem |c G.J.O. Jameson |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a X, 252 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society student texts |v 53 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Nombres premiers | |
| 650 | 4 | |a Numbers, Prime | |
| 650 | 0 | 7 | |a Primzahl |0 (DE-588)4047263-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Primzahltheorie |0 (DE-588)4175715-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Primzahl |0 (DE-588)4047263-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Primzahltheorie |0 (DE-588)4175715-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a London Mathematical Society student texts |v 53 |w (DE-604)BV000841726 |9 53 | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/cam031/2002074199.html |3 Table of contents | |
| 856 | 4 | |u http://www.loc.gov/catdir/description/cam0210/2002074199.html |3 Publisher description | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009940641 | ||
Datensatz im Suchindex
| _version_ | 1804129402129219584 |
|---|---|
| adam_text | Contents
Preface page vii
1 Foundations 1
1.1 Counting prime numbers 2
1.2 Arithmetic functions 6
1.3 Abel summation 9
1.4 Estimation of sums by integrals; Euler s summation formula 18
1.5 The function i{x) 28
1.6 Chebyshev s theta function 33
1.7 Dirichlet series and the zeta function 38
1.8 Convolutions 50
2 Some important Dirichlet series and arithmetic functions 56
2.1 The Euler product 57
2.2 The Mobius function 61
2.3 The series for logC(s) and C («)/C(s) 70
2.4 Chebyshev s psi function and powers of primes 75
2.5 Estimates of some summation functions 82
2.6 Mertens s estimates 89
3 The basic theorems 98
3.1 Extension of the definition of the zeta function 99
3.2 Inversion of Dirichlet series; the integral version of the
fundamental theorem 114
3.3 An alternative method: Newman s proof 124
3.4 The limit and series versions of the fundamental theorem;
the prime number theorem 130
3.5 Some applications of the prime number theorem 138
4 Prime numbers in residue classes: Dirichlet s theorem 147
4.1 Characters of finite abelian groups 148
v
vi Contents
4.2 Dirichlet characters 153
4.3 Dirichlet L functions 160
4.4 Prime numbers in residue classes 173
5 Error estimates and the Riemann hypothesis 178
5.1 Error estimates 179
5.2 Connections with the Riemann hypothesis 192
5.3 The zero free region of the zeta function 195
6 An elementary proof of the prime number theorem 206
6.1 Framework of the proof 207
6.2 Selberg s formulae and completion of the proof 212
Appendices
A Complex functions of a real variable 223
B Double series and multiplication of series 225
C Infinite products 228
D Differentiation under the integral sign 230
E The O, o notation 232
F Computing values of ir(x) 234
G Table of primes 238
H Biographical notes 240
Bibliography 249
Index 251
|
| any_adam_object | 1 |
| author | Jameson, Graham J. O. |
| author_facet | Jameson, Graham J. O. |
| author_role | aut |
| author_sort | Jameson, Graham J. O. |
| author_variant | g j o j gjo gjoj |
| building | Verbundindex |
| bvnumber | BV014630034 |
| callnumber-first | Q - Science |
| callnumber-label | QA246 |
| callnumber-raw | QA246 |
| callnumber-search | QA246 |
| callnumber-sort | QA 3246 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| classification_tum | MAT 100f |
| ctrlnum | (OCoLC)50253282 (DE-599)BVBBV014630034 |
| dewey-full | 512/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.72 |
| dewey-search | 512/.72 |
| dewey-sort | 3512 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01983nam a2200517zcb4500</leader><controlfield tag="001">BV014630034</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150205 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020731s2003 xxk |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2002074199</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521814111</subfield><subfield code="9">0-521-81411-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521891108</subfield><subfield code="9">0-521-89110-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)50253282</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014630034</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxk</subfield><subfield code="c">GB</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA246</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.72</subfield><subfield code="2">21</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">MAT 100f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jameson, Graham J. O.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The prime number theorem</subfield><subfield code="c">G.J.O. Jameson</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 252 S.</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">London Mathematical Society student texts</subfield><subfield code="v">53</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nombres premiers</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numbers, Prime</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Primzahl</subfield><subfield code="0">(DE-588)4047263-2</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">Primzahl</subfield><subfield code="0">(DE-588)4047263-2</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">Primzahltheorie</subfield><subfield code="0">(DE-588)4175715-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society student texts</subfield><subfield code="v">53</subfield><subfield code="w">(DE-604)BV000841726</subfield><subfield code="9">53</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/toc/cam031/2002074199.html</subfield><subfield code="3">Table of contents</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/description/cam0210/2002074199.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=009940641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009940641</subfield></datafield></record></collection> |
| id | DE-604.BV014630034 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:04:34Z |
| institution | BVB |
| isbn | 0521814111 0521891108 |
| language | English |
| lccn | 2002074199 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009940641 |
| oclc_num | 50253282 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-188 DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-188 DE-384 |
| physical | X, 252 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Jameson, Graham J. O. Verfasser aut The prime number theorem G.J.O. Jameson 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2003 X, 252 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 53 Hier auch später erschienene, unveränderte Nachdrucke Nombres premiers Numbers, Prime Primzahl (DE-588)4047263-2 gnd rswk-swf Primzahltheorie (DE-588)4175715-4 gnd rswk-swf Primzahl (DE-588)4047263-2 s DE-604 Primzahltheorie (DE-588)4175715-4 s London Mathematical Society student texts 53 (DE-604)BV000841726 53 http://www.loc.gov/catdir/toc/cam031/2002074199.html Table of contents http://www.loc.gov/catdir/description/cam0210/2002074199.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jameson, Graham J. O. The prime number theorem London Mathematical Society student texts Nombres premiers Numbers, Prime Primzahl (DE-588)4047263-2 gnd Primzahltheorie (DE-588)4175715-4 gnd |
| subject_GND | (DE-588)4047263-2 (DE-588)4175715-4 |
| title | The prime number theorem |
| title_auth | The prime number theorem |
| title_exact_search | The prime number theorem |
| title_full | The prime number theorem G.J.O. Jameson |
| title_fullStr | The prime number theorem G.J.O. Jameson |
| title_full_unstemmed | The prime number theorem G.J.O. Jameson |
| title_short | The prime number theorem |
| title_sort | the prime number theorem |
| topic | Nombres premiers Numbers, Prime Primzahl (DE-588)4047263-2 gnd Primzahltheorie (DE-588)4175715-4 gnd |
| topic_facet | Nombres premiers Numbers, Prime Primzahl Primzahltheorie |
| url | http://www.loc.gov/catdir/toc/cam031/2002074199.html http://www.loc.gov/catdir/description/cam0210/2002074199.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000841726 |
| work_keys_str_mv | AT jamesongrahamjo theprimenumbertheorem |