The great prime number race:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2020]
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| Schriftenreihe: | Student mathematical library
volume 92 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xii, 138 Seiten Diagramme |
| ISBN: | 9781470462574 |
Internformat
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| 653 | 0 | |a Number theory -- Zeta and $L$-functions: analytic theory -- $\zeta (s)$ and $L(s, \chi)$_ | |
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Datensatz im Suchindex
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| adam_text | Contents Preface ix Chapter 1. The Riemann zeta function 1 §1.1. §1.2. Introduction 1 The Riemann zeta function §1.3. The prime numbers 3 4 §1-4. The Riemann zeta function 6 §1-5. Euler and the zeta function 8 §1.6. Meromorphic continuation of ζ(s) Chapter 2. The Euler product 10 §2.1. The zeta function and the Euler product 17 17 §2.2. The logarithmic derivative of Հ(տ) 20 Chapter 3. The functional equation §3.1. The gamma function 27 29 §3.2. §3.3. The functional equation 36 Some zeta values 41 §3.4. Euler and the functional equation 43 §3.5. The Euler constant revisited 47 vii
viii Contents Chapter 4. The explicit formulas in analytic number theory 57 §4.1. The von Mangoldt explicit formula 58 §4.2. Can you hear the Riemann hypothesis? 61 §4.3. Comparison with Fourier series 63 §4.4. Proof of the von Mangoldt formula 65 §4.5. The logarithmic integral Li(z) 69 §4.6. The Riemann formula 73 §4.7. Origin of the Riemann explicit formula 78 Chapter 5. The prime number theorem 81 §5.1. The Riemann-Ramanujan approximation 81 §5.2. Proof of the prime number theorem 82 Chapter 6. Oscillation of π{χ) — Li(x) 93 §6.1. Littlewood’s theorem 93 §6.2. Lehman’s theorem 98 Chapter 7. The prime number race 107 §7.1. On the logarithmic density 107 §7.2. Upper bounds for the Skewes number 109 Chapter 8. Exercises, hints, and selected solutions §8.1. Exercises §8.2. Hints and selected solutions 113 113 120 Bibliography 133 Index 137
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| adam_txt |
Contents Preface ix Chapter 1. The Riemann zeta function 1 §1.1. §1.2. Introduction 1 The Riemann zeta function §1.3. The prime numbers 3 4 §1-4. The Riemann zeta function 6 §1-5. Euler and the zeta function 8 §1.6. Meromorphic continuation of ζ(s) Chapter 2. The Euler product 10 §2.1. The zeta function and the Euler product 17 17 §2.2. The logarithmic derivative of Հ(տ) 20 Chapter 3. The functional equation §3.1. The gamma function 27 29 §3.2. §3.3. The functional equation 36 Some zeta values 41 §3.4. Euler and the functional equation 43 §3.5. The Euler constant revisited 47 vii
viii Contents Chapter 4. The explicit formulas in analytic number theory 57 §4.1. The von Mangoldt explicit formula 58 §4.2. Can you hear the Riemann hypothesis? 61 §4.3. Comparison with Fourier series 63 §4.4. Proof of the von Mangoldt formula 65 §4.5. The logarithmic integral Li(z) 69 §4.6. The Riemann formula 73 §4.7. Origin of the Riemann explicit formula 78 Chapter 5. The prime number theorem 81 §5.1. The Riemann-Ramanujan approximation 81 §5.2. Proof of the prime number theorem 82 Chapter 6. Oscillation of π{χ) — Li(x) 93 §6.1. Littlewood’s theorem 93 §6.2. Lehman’s theorem 98 Chapter 7. The prime number race 107 §7.1. On the logarithmic density 107 §7.2. Upper bounds for the Skewes number 109 Chapter 8. Exercises, hints, and selected solutions §8.1. Exercises §8.2. Hints and selected solutions 113 113 120 Bibliography 133 Index 137 |
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| spelling | Plymen, Roger J. (DE-588)1158264356 aut The great prime number race Roger Plymen Providence, Rhode Island American Mathematical Society [2020] xii, 138 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 92 Includes bibliographical references and index Primzahl (DE-588)4047263-2 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Numbers, Prime Number theory Number theory -- Historical (must also be assigned at least one classification number from Section 01) Number theory -- Elementary number theory {For analogues in number fields, see 11R04} -- Primes Number theory -- Zeta and $L$-functions: analytic theory -- $\zeta (s)$ and $L(s, \chi)$_ Number theory -- Multiplicative number theory -- Distribution of primes Zahlentheorie (DE-588)4067277-3 s Primzahl (DE-588)4047263-2 s DE-604 9781470462796 Erscheint auch als Online-Ausgabe Plymen, Roger The Great Prime Number Race Providence : American Mathematical Society, 2020 1 online resource (153 pages) 9781470462796 Student mathematical library volume 92 (DE-604)BV013184751 92 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032424693&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Plymen, Roger J. The great prime number race Student mathematical library Primzahl (DE-588)4047263-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4047263-2 (DE-588)4067277-3 |
| title | The great prime number race |
| title_auth | The great prime number race |
| title_exact_search | The great prime number race |
| title_exact_search_txtP | The great prime number race |
| title_full | The great prime number race Roger Plymen |
| title_fullStr | The great prime number race Roger Plymen |
| title_full_unstemmed | The great prime number race Roger Plymen |
| title_short | The great prime number race |
| title_sort | the great prime number race |
| topic | Primzahl (DE-588)4047263-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Primzahl Zahlentheorie |
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