Prime numbers and the Riemann hypothesis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY, USA
Cambridge University Press
[2016]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xi, 142 Seiten Illustrationen, Diagramme (überwiegend farbig) |
| ISBN: | 9781107101920 9781107499430 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface page vii
PART I. The Riemann Hypothesis 1
1 Thoughts About Numbers 3
2 What are Prime Numbers? 6
3 “Named” Prime Numbers 11
4 Sieves 13
5 Questions About Primes 16
6 Further Questions About Primes 19
7 How Many Primes are There? 23
8 Prime Numbers Viewed from a Distance 28
9 Pure and Applied Mathematics 30
10 A Probabilistic First Guess 32
11 What is a “Good Approximation”? 36
12 Square Root Error and Random Walks 38
13 What is Riemann’s Hypothesis? 40
14 The Mystery Moves to the Error Term 42
15 Cesàro Smoothing 43
16 AViewof |Li(X) - k(X) 45
17 The Prime Number Theorem 47
18 The Staircase of Primes 51
v
19 Tinkering with the Staircase of Primes 53
20 Computer Music Files and Prime Numbers 56
21 The Word “Spectrum” 62
22 Spectra and Trigonometric Sums 64
23 The Spectrum and the Staircase of Primes 66
24 To Our Readers of Part I 67
PART II. Distributions 69
25 Slopes of Graphs That Have No Slopes 71
26 Distributions 77
27 Fourier Transforms: Second Visit 82
28 Fourier Transform of Delta 85
29 Trigonometric Series 87
30 A Sneak Preview of Part III 89
PART III. The Riemann Spectrum of the Prime Numbers 95
31 On Losing No Information 97
32 From Primes to the Riemann Spectrum 99
33 How Many 0/s are There? 104
34 Further Questions About the Riemann Spectrum 106
35 From the Riemann Spectrum to Primes 108
PART IV. Back to Riemann 111
36 Building n (X) from the Spectrum 113
37 As Riemann Envisioned It 119
38 Companions to the Zeta Function 125
Endnotes 129
Index 141
PRIME NUMBERS AND THE RIEMANN
HYPOTHESIS
Prime numbers are beautiful, mysterious, and beguiling mathematical
objects. The mathematician Bernhard Riemann made a celebrated con-
jecture about primes in 1859, the so-called Riemann Hypothesis, which
remains to be one of the most important unsolved problems in mathe-
matics. Through the deep insights of the authors, this book introduces
primes and explains the Riemann Hypothesis.
Students with minimal mathematical background and scholars alike
will enjoy this comprehensive discussion of primes. The first part of the
book will inspire the curiosity of a general reader with an accessible
explanation of the key ideas. The exposition of these ideas is generously
illuminated by computational graphics that exhibit the key concepts
and phenomena in enticing detail. Readers with more mathematical
experience will then go deeper into the structure of primes and see how
the Riemann Hypothesis relates to Fourier analysis using the vocabu-
lary of spectra. Readers with a strong mathematical background will be
able to connect these ideas to historical formulations of the Riemann
Hypothesis.
Barry Mazur is the Gerhard Gade University Professor at Harvard Uni-
versity. He is the author of Imagining Numbers (particularly the square
root of minus fifteen) and coeditor, with Apostólos Doxiadis, of Circles
Disturbed: The Interplay of Mathematics and Narrative.
William Stein is Professor of Mathematics at the University of
Washington. Author of Elementary Number Theory: Primes, Congru-
ences, and Secrets: A Computational Approach, he is also the founder
of the Sage mathematical software project.
|
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| dewey-full | 512.7/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:12:30Z |
| institution | BVB |
| isbn | 9781107101920 9781107499430 |
| language | English |
| lccn | 015018981 |
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| spelling | Mazur, Barry 1937- Verfasser (DE-588)107715945 aut Prime numbers and the Riemann hypothesis Barry Mazur, Harvard University, Cambridge, MA, USA, William Stein, University of Washington, Seattle, WA, USA New York, NY, USA Cambridge University Press [2016] xi, 142 Seiten Illustrationen, Diagramme (überwiegend farbig) txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Riemann hypothesis Numbers, Prime Primzahl (DE-588)4047263-2 gnd rswk-swf Riemannsche Vermutung (DE-588)4704537-1 gnd rswk-swf Primzahl (DE-588)4047263-2 s Riemannsche Vermutung (DE-588)4704537-1 s DE-604 Stein, William 1974- Verfasser (DE-588)137841973 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028333382&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028333382&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mazur, Barry 1937- Stein, William 1974- Prime numbers and the Riemann hypothesis Riemann hypothesis Numbers, Prime Primzahl (DE-588)4047263-2 gnd Riemannsche Vermutung (DE-588)4704537-1 gnd |
| subject_GND | (DE-588)4047263-2 (DE-588)4704537-1 |
| title | Prime numbers and the Riemann hypothesis |
| title_auth | Prime numbers and the Riemann hypothesis |
| title_exact_search | Prime numbers and the Riemann hypothesis |
| title_full | Prime numbers and the Riemann hypothesis Barry Mazur, Harvard University, Cambridge, MA, USA, William Stein, University of Washington, Seattle, WA, USA |
| title_fullStr | Prime numbers and the Riemann hypothesis Barry Mazur, Harvard University, Cambridge, MA, USA, William Stein, University of Washington, Seattle, WA, USA |
| title_full_unstemmed | Prime numbers and the Riemann hypothesis Barry Mazur, Harvard University, Cambridge, MA, USA, William Stein, University of Washington, Seattle, WA, USA |
| title_short | Prime numbers and the Riemann hypothesis |
| title_sort | prime numbers and the riemann hypothesis |
| topic | Riemann hypothesis Numbers, Prime Primzahl (DE-588)4047263-2 gnd Riemannsche Vermutung (DE-588)4704537-1 gnd |
| topic_facet | Riemann hypothesis Numbers, Prime Primzahl Riemannsche Vermutung |
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