The prime number theorem /:
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The p...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2003.
|
| Schriftenreihe: | London Mathematical Society student texts ;
53. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material. |
| Beschreibung: | 1 online resource (x, 252 pages) |
| Bibliographie: | Includes bibliographical references (pages 249-250) and index. |
| ISBN: | 9781139164986 1139164988 9780511078194 0511078196 9780511076626 0511076622 9781107101470 1107101476 |
Internformat
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| 520 | |a At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material. | ||
| 505 | 0 | 0 | |g 1. |t Foundations -- |g 2. |t Some important Dirichlet series and arithmetic functions -- |g 3. |t basic theorems -- |g 4. |t Prime numbers in residue classes: Dirichlet's theorem -- |g 5. |t Error estimates and the Riemann hypothesis -- |g 6. |t "elementary" proof of the prime number theorem -- |g App. A. |t Complex functions of a real variable -- |g App. B. |t Double series and multiplication of series -- |g App. C. |t Infinite products -- |g App. D. |t Differentiation under the integral sign -- |g App. E. |t O, o notation -- |g App. F. |t Computing values of [pi](x) -- |g App. G. |t Table of primes -- |g App. H. |t Biographical notes. |
| 650 | 0 | |a Numbers, Prime. |0 http://id.loc.gov/authorities/subjects/sh85093218 | |
| 650 | 6 | |a Nombres premiers. | |
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Datensatz im Suchindex
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| _version_ | 1813903592143192064 |
| adam_text | |
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| author | Jameson, G. J. O. (Graham James Oscar) |
| author_GND | http://id.loc.gov/authorities/names/n86036513 |
| author_facet | Jameson, G. J. O. (Graham James Oscar) |
| author_role | |
| author_sort | Jameson, G. J. O. |
| author_variant | g j o j gjo gjoj |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
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| callnumber-raw | QA246 .J36 2003eb |
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| callnumber-subject | QA - Mathematics |
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| contents | Foundations -- Some important Dirichlet series and arithmetic functions -- basic theorems -- Prime numbers in residue classes: Dirichlet's theorem -- Error estimates and the Riemann hypothesis -- "elementary" proof of the prime number theorem -- Complex functions of a real variable -- Double series and multiplication of series -- Infinite products -- Differentiation under the integral sign -- O, o notation -- Computing values of [pi](x) -- Table of primes -- Biographical notes. |
| ctrlnum | (OCoLC)817922016 |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.72 |
| dewey-sort | 3512 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-10-25T16:21:08Z |
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| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Jameson, G. J. O. (Graham James Oscar) https://id.oclc.org/worldcat/entity/E39PCjymTyFXDWHphxdjfYXQmb http://id.loc.gov/authorities/names/n86036513 The prime number theorem / G.J.O. Jameson. Cambridge ; New York : Cambridge University Press, 2003. 1 online resource (x, 252 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 53 Includes bibliographical references (pages 249-250) and index. Print version record. At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material. 1. Foundations -- 2. Some important Dirichlet series and arithmetic functions -- 3. basic theorems -- 4. Prime numbers in residue classes: Dirichlet's theorem -- 5. Error estimates and the Riemann hypothesis -- 6. "elementary" proof of the prime number theorem -- App. A. Complex functions of a real variable -- App. B. Double series and multiplication of series -- App. C. Infinite products -- App. D. Differentiation under the integral sign -- App. E. O, o notation -- App. F. Computing values of [pi](x) -- App. G. Table of primes -- App. H. Biographical notes. Numbers, Prime. http://id.loc.gov/authorities/subjects/sh85093218 Nombres premiers. MATHEMATICS Number Theory. bisacsh Numbers, Prime fast Primzahl gnd http://d-nb.info/gnd/4047263-2 Primzahltheorie gnd http://d-nb.info/gnd/4175715-4 has work: The prime number theorem (Text) https://id.oclc.org/worldcat/entity/E39PCFJT64grQ3bjp6M3XgbqV3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Jameson, G.J.O. (Graham James Oscar). Prime number theorem. Cambridge ; New York : Cambridge University Press, 2003 0521814111 (DLC) 2002074199 (OCoLC)50253282 London Mathematical Society student texts ; 53. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=125089 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=125089 Volltext |
| spellingShingle | Jameson, G. J. O. (Graham James Oscar) The prime number theorem / London Mathematical Society student texts ; Foundations -- Some important Dirichlet series and arithmetic functions -- basic theorems -- Prime numbers in residue classes: Dirichlet's theorem -- Error estimates and the Riemann hypothesis -- "elementary" proof of the prime number theorem -- Complex functions of a real variable -- Double series and multiplication of series -- Infinite products -- Differentiation under the integral sign -- O, o notation -- Computing values of [pi](x) -- Table of primes -- Biographical notes. Numbers, Prime. http://id.loc.gov/authorities/subjects/sh85093218 Nombres premiers. MATHEMATICS Number Theory. bisacsh Numbers, Prime fast Primzahl gnd http://d-nb.info/gnd/4047263-2 Primzahltheorie gnd http://d-nb.info/gnd/4175715-4 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85093218 http://d-nb.info/gnd/4047263-2 http://d-nb.info/gnd/4175715-4 |
| title | The prime number theorem / |
| title_alt | Foundations -- Some important Dirichlet series and arithmetic functions -- basic theorems -- Prime numbers in residue classes: Dirichlet's theorem -- Error estimates and the Riemann hypothesis -- "elementary" proof of the prime number theorem -- Complex functions of a real variable -- Double series and multiplication of series -- Infinite products -- Differentiation under the integral sign -- O, o notation -- Computing values of [pi](x) -- Table of primes -- Biographical notes. |
| 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 | prime number theorem |
| topic | Numbers, Prime. http://id.loc.gov/authorities/subjects/sh85093218 Nombres premiers. MATHEMATICS Number Theory. bisacsh Numbers, Prime fast Primzahl gnd http://d-nb.info/gnd/4047263-2 Primzahltheorie gnd http://d-nb.info/gnd/4175715-4 |
| topic_facet | Numbers, Prime. Nombres premiers. MATHEMATICS Number Theory. Numbers, Prime Primzahl Primzahltheorie |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=125089 |
| work_keys_str_mv | AT jamesongjo theprimenumbertheorem AT jamesongjo primenumbertheorem |