The Riemann hypothesis: a resource for the afficionado and virtuoso alike
Saved in:
| Other Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | CMS books in mathematics
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seiten [483] - 500 |
| Physical Description: | XIV, 533 Seiten Illustrationen, Diagramme |
| ISBN: | 9780387721255 0387721258 |
Staff View
MARC
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| 245 | 1 | 0 | |a The Riemann hypothesis |b a resource for the afficionado and virtuoso alike |c Peter Borwein, Stephen Choi, Brendan Rooney and Andrea Weirathmueller (Eds.) |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XIV, 533 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a CMS books in mathematics |v 27 | |
| 500 | |a Literaturverzeichnis Seiten [483] - 500 | ||
| 600 | 1 | 4 | |a Riemann, Bernhard <1826-1866> |
| 600 | 1 | 4 | |a Riemann, Bernhard <1826-1866> |
| 648 | 7 | |a Geschichte |2 gnd |9 rswk-swf | |
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| 650 | 4 | |a Riemann hypothesis | |
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Contents
Part I Introduction to the Riemann Hypothesis
1
Why This Book
. 3
1.1
The Holy Grail
. 3
1.2
Riemann's
Zeta
and Liouville's Lambda
. 5
1.3
The Prime Number Theorem
. 7
2
Analytic Prelimmaries
. 9
2.1
The Riemann
Zeta
Function
. 9
2.2
Zero-free Region
. 16
2.3
Counting the Zeros of ((s)
. 18
2.4
Hardy's Theorem
. 24
3
Algorithms for Calculating C(s)
. 29
3.1
Euler-MacLaurin Summation
. 29
3.2
Backlund
. 30
3.3
Hardy's Function
. 31
3.4
The Riemann-Siegel Formula
. 32
3.5
Gram's Law
. 33
3.6
Turing
. 34
3.7
The
Odlyzko-Schönhage
Algorithm
. 35
3.8
A Simple Algorithm for the
Zeta
Function
. 35
3.9
Further Reading
. 36
X
Contents
4
Empirical Evidence
. 37
4.1
Verification in an Interval
. 37
4.2
A Brief History of Computational Evidence
. 39
4.3
The Riemann Hypothesis and Random Matrices
. 40
4.4
The Skewes Number
. 43
5
Equivalent Statements
. 45
5.1
Number-Theoretic Equivalences
. 45
5.2
Analytic Equivalences
. 49
5.3
Other Equivalences
. 52
6
Extensions of the Riemann Hypothesis
. 55
6.1
The Riemann Hypothesis
. 55
6.2
The Generalized Riemann Hypothesis
. 56
6.3
The Extended Riemann Hypothesis
. 57
6.4
An Equivalent Extended Riemann Hypothesis
. 57
6.5
Another Extended Riemann Hypothesis
. 58
6.6
The Grand Riemann Hypothesis
. 58
7
Assuming the Riemann Hypothesis and Its Extensions
. 61
7.1
Another Proof of The Prime Number Theorem
. 61
7.2
Goldbach's Conjecture
. 62
7.3
More
Goldbach. 62
7.4
Primes in a Given Interval
. 63
7.5
The Least Prime in Arithmetic Progressions
. 63
7.6
Primality Testing
. 63
7.7
Artin's Primitive Root Conjecture
. 64
7.8
Bounds on Dirichlet L-Series
. 64
7.9
The
Lindelof
Hypothesis
. 65
7.10
Titchmarsh's
ЦТ)
Function
. 65
7.11
Mean Values of C(s)
. 66
8
Failed Attempts at Proof
. 69
8.1
Stieltjes
and Mertens' Conjecture
. 69
8.2
Hans Rademacher and False Hopes
. 70
8.3
Turán's
Condition
. 71
8.4
Louis
de Branges's
Approach
. 71
8.5
No Really Good Idea
. 72
Contents
XI
9
Formulas
. 73
10 Timeline. 81
Part II
Original
Papers
11
Expert Witnesses
. 93
11.1
E. Bombierì
(2000-2001). 94
11.2
P.
Sárnak
(2004).106
11.3
J. B.
Conrey
(2003) .116
11.4
A. Ivić
(2003) .130
12
The Experts Speak for Themselves
.161
12.1
P. L. Chebyshev
(1852).162
12.2
B. Riemann
(1859).183
12.3
J.
Hadamard
(1896).199
12.4
С.
de la Vallèe
Poussin
(1899) .222
12.5
G. H. Hardy
(1914) .296
12.6
G. H. Hardy
(1915) .300
12.7
G. H. Hardy and J. E. Littlewood
(1915).307
12.8
A.
Weil (1941).313
12.9
P.
Turan
(1948).317
12.10
A. Selberg
(1949) .353
12.11
P.
Erdős
(1949).363
12.12
S. Skewes
(1955).375
12.13
С. В.
Haselgrove
(1958).399
12.14
H.
Montgomery
(1973).405
12.15
D. J.
Newman
(1980).419
12.16
J.
Korevaar
(1982).424
12.17
H. Daboussi
(1984).433
12.18
Α.
Hildebrand (1986).438
12.19
D.
Goldston
and H.
Montgomery
(1987) .447
12.20
M. AgrawaI,
N.
Kayal, and
N.
Saxena
(2004) .469
References
.483
References.
491
Index
.501 |
| adam_txt |
Contents
Part I Introduction to the Riemann Hypothesis
1
Why This Book
. 3
1.1
The Holy Grail
. 3
1.2
Riemann's
Zeta
and Liouville's Lambda
. 5
1.3
The Prime Number Theorem
. 7
2
Analytic Prelimmaries
. 9
2.1
The Riemann
Zeta
Function
. 9
2.2
Zero-free Region
. 16
2.3
Counting the Zeros of ((s)
. 18
2.4
Hardy's Theorem
. 24
3
Algorithms for Calculating C(s)
. 29
3.1
Euler-MacLaurin Summation
. 29
3.2
Backlund
. 30
3.3
Hardy's Function
. 31
3.4
The Riemann-Siegel Formula
. 32
3.5
Gram's Law
. 33
3.6
Turing
. 34
3.7
The
Odlyzko-Schönhage
Algorithm
. 35
3.8
A Simple Algorithm for the
Zeta
Function
. 35
3.9
Further Reading
. 36
X
Contents
4
Empirical Evidence
. 37
4.1
Verification in an Interval
. 37
4.2
A Brief History of Computational Evidence
. 39
4.3
The Riemann Hypothesis and Random Matrices
. 40
4.4
The Skewes Number
. 43
5
Equivalent Statements
. 45
5.1
Number-Theoretic Equivalences
. 45
5.2
Analytic Equivalences
. 49
5.3
Other Equivalences
. 52
6
Extensions of the Riemann Hypothesis
. 55
6.1
The Riemann Hypothesis
. 55
6.2
The Generalized Riemann Hypothesis
. 56
6.3
The Extended Riemann Hypothesis
. 57
6.4
An Equivalent Extended Riemann Hypothesis
. 57
6.5
Another Extended Riemann Hypothesis
. 58
6.6
The Grand Riemann Hypothesis
. 58
7
Assuming the Riemann Hypothesis and Its Extensions
. 61
7.1
Another Proof of The Prime Number Theorem
. 61
7.2
Goldbach's Conjecture
. 62
7.3
More
Goldbach. 62
7.4
Primes in a Given Interval
. 63
7.5
The Least Prime in Arithmetic Progressions
. 63
7.6
Primality Testing
. 63
7.7
Artin's Primitive Root Conjecture
. 64
7.8
Bounds on Dirichlet L-Series
. 64
7.9
The
Lindelof
Hypothesis
. 65
7.10
Titchmarsh's
ЦТ)
Function
. 65
7.11
Mean Values of C(s)
. 66
8
Failed Attempts at Proof
. 69
8.1
Stieltjes
and Mertens' Conjecture
. 69
8.2
Hans Rademacher and False Hopes
. 70
8.3
Turán's
Condition
. 71
8.4
Louis
de Branges's
Approach
. 71
8.5
No Really Good Idea
. 72
Contents
XI
9
Formulas
. 73
10 Timeline. 81
Part II
Original
Papers
11
Expert Witnesses
. 93
11.1
E. Bombierì
(2000-2001). 94
11.2
P.
Sárnak
(2004).106
11.3
J. B.
Conrey
(2003) .116
11.4
A. Ivić
(2003) .130
12
The Experts Speak for Themselves
.161
12.1
P. L. Chebyshev
(1852).162
12.2
B. Riemann
(1859).183
12.3
J.
Hadamard
(1896).199
12.4
С.
de la Vallèe
Poussin
(1899) .222
12.5
G. H. Hardy
(1914) .296
12.6
G. H. Hardy
(1915) .300
12.7
G. H. Hardy and J. E. Littlewood
(1915).307
12.8
A.
Weil (1941).313
12.9
P.
Turan
(1948).317
12.10
A. Selberg
(1949) .353
12.11
P.
Erdős
(1949).363
12.12
S. Skewes
(1955).375
12.13
С. В.
Haselgrove
(1958).399
12.14
H.
Montgomery
(1973).405
12.15
D. J.
Newman
(1980).419
12.16
J.
Korevaar
(1982).424
12.17
H. Daboussi
(1984).433
12.18
Α.
Hildebrand (1986).438
12.19
D.
Goldston
and H.
Montgomery
(1987) .447
12.20
M. AgrawaI,
N.
Kayal, and
N.
Saxena
(2004) .469
References
.483
References.
491
Index
.501 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author2 | Borwein, Peter B. 1953-2020 Choi, Stephen |
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| building | Verbundindex |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512.7/3 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| era | Geschichte gnd |
| era_facet | Geschichte |
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| id | DE-604.BV023096280 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:43:12Z |
| indexdate | 2025-01-28T11:10:57Z |
| institution | BVB |
| isbn | 9780387721255 0387721258 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016299076 |
| oclc_num | 190760103 |
| open_access_boolean | |
| owner | DE-824 DE-20 DE-29T DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-188 DE-739 DE-83 |
| owner_facet | DE-824 DE-20 DE-29T DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-188 DE-739 DE-83 |
| physical | XIV, 533 Seiten Illustrationen, Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | CMS books in mathematics |
| series2 | CMS books in mathematics |
| spelling | The Riemann hypothesis a resource for the afficionado and virtuoso alike Peter Borwein, Stephen Choi, Brendan Rooney and Andrea Weirathmueller (Eds.) New York, NY Springer 2008 XIV, 533 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier CMS books in mathematics 27 Literaturverzeichnis Seiten [483] - 500 Riemann, Bernhard <1826-1866> Geschichte gnd rswk-swf Nombres premiers Riemann, Hypothèse de Théorie des nombres Number theory Numbers, Prime Riemann hypothesis Riemannsche Vermutung (DE-588)4704537-1 gnd rswk-swf (DE-588)4135952-5 Quelle gnd-content Riemannsche Vermutung (DE-588)4704537-1 s DE-604 Geschichte z Borwein, Peter B. 1953-2020 (DE-588)1018056440 edt Choi, Stephen (DE-588)1210935961 edt Rooney, Brendan Sonstige oth CMS books in mathematics 27 (DE-604)BV013248581 27 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016299076&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The Riemann hypothesis a resource for the afficionado and virtuoso alike CMS books in mathematics Riemann, Bernhard <1826-1866> Nombres premiers Riemann, Hypothèse de Théorie des nombres Number theory Numbers, Prime Riemann hypothesis Riemannsche Vermutung (DE-588)4704537-1 gnd |
| subject_GND | (DE-588)4704537-1 (DE-588)4135952-5 |
| title | The Riemann hypothesis a resource for the afficionado and virtuoso alike |
| title_auth | The Riemann hypothesis a resource for the afficionado and virtuoso alike |
| title_exact_search | The Riemann hypothesis a resource for the afficionado and virtuoso alike |
| title_exact_search_txtP | The Riemann hypothesis a resource for the afficionado and virtuoso alike |
| title_full | The Riemann hypothesis a resource for the afficionado and virtuoso alike Peter Borwein, Stephen Choi, Brendan Rooney and Andrea Weirathmueller (Eds.) |
| title_fullStr | The Riemann hypothesis a resource for the afficionado and virtuoso alike Peter Borwein, Stephen Choi, Brendan Rooney and Andrea Weirathmueller (Eds.) |
| title_full_unstemmed | The Riemann hypothesis a resource for the afficionado and virtuoso alike Peter Borwein, Stephen Choi, Brendan Rooney and Andrea Weirathmueller (Eds.) |
| title_short | The Riemann hypothesis |
| title_sort | the riemann hypothesis a resource for the afficionado and virtuoso alike |
| title_sub | a resource for the afficionado and virtuoso alike |
| topic | Riemann, Bernhard <1826-1866> Nombres premiers Riemann, Hypothèse de Théorie des nombres Number theory Numbers, Prime Riemann hypothesis Riemannsche Vermutung (DE-588)4704537-1 gnd |
| topic_facet | Riemann, Bernhard <1826-1866> Nombres premiers Riemann, Hypothèse de Théorie des nombres Number theory Numbers, Prime Riemann hypothesis Riemannsche Vermutung Quelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016299076&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013248581 |
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