The prime number theorem:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society student texts
53 |
| Subjects: | |
| Online Access: | Table of contents Publisher description Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | X, 252 S. |
| ISBN: | 0521814111 0521891108 |
Staff View
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Record in the Search Index
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| 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
|
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| language | English |
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| physical | X, 252 S. |
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| publisher | Cambridge Univ. Press |
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| 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 |
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