Multiplicative number theory I: classical theory
Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the mo...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schriftenreihe: | Cambridge studies in advanced mathematics
97 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xvii, 552 Seiten) |
| ISBN: | 9780511618314 |
| DOI: | 10.1017/CBO9780511618314 |
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| 505 | 8 | |a Dirichlet series I -- The elementary theory of arithmetic functions -- Principles and first examples of sieve methods -- Primes in arithmetic progressions I -- Dirichlet series II -- The prime number theorem -- Applications of the prime number theorem -- Further discussion of the prime number theorem -- Primitive characters and Gauss sums -- Analytic properties of the zeta function and L-functions -- Primes in arithmetic progressions II -- Explicit formulae -- Conditional estimates -- Zeros -- Oscillations of error terms -- Appendices. A. The Riemann-Stieltjes integral; B. Bernoulli numbers and the Euler-MacLaurin summation formula; C. The gamma function; D. Topics in harmonic analysis | |
| 520 | |a Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises | ||
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Datensatz im Suchindex
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| author | Montgomery, Hugh L. 1944- |
| author_GND | (DE-588)172262968 (DE-588)1057557110 |
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| author_sort | Montgomery, Hugh L. 1944- |
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| building | Verbundindex |
| bvnumber | BV043940615 |
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| contents | Dirichlet series I -- The elementary theory of arithmetic functions -- Principles and first examples of sieve methods -- Primes in arithmetic progressions I -- Dirichlet series II -- The prime number theorem -- Applications of the prime number theorem -- Further discussion of the prime number theorem -- Primitive characters and Gauss sums -- Analytic properties of the zeta function and L-functions -- Primes in arithmetic progressions II -- Explicit formulae -- Conditional estimates -- Zeros -- Oscillations of error terms -- Appendices. A. The Riemann-Stieltjes integral; B. Bernoulli numbers and the Euler-MacLaurin summation formula; C. The gamma function; D. Topics in harmonic analysis |
| ctrlnum | (ZDB-20-CBO)CR9780511618314 (OCoLC)967678951 (DE-599)BVBBV043940615 |
| dewey-full | 512.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.723 |
| dewey-search | 512.723 |
| dewey-sort | 3512.723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511618314 |
| format | Electronic eBook |
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| id | DE-604.BV043940615 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9780511618314 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349585 |
| oclc_num | 967678951 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| physical | 1 Online-Ressource (xvii, 552 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Montgomery, Hugh L. 1944- Verfasser (DE-588)172262968 aut Multiplicative number theory I classical theory Hugh L. Montgomery, Robert C. Vaughn Cambridge Cambridge University Press 2007 1 Online-Ressource (xvii, 552 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 97 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Dirichlet series I -- The elementary theory of arithmetic functions -- Principles and first examples of sieve methods -- Primes in arithmetic progressions I -- Dirichlet series II -- The prime number theorem -- Applications of the prime number theorem -- Further discussion of the prime number theorem -- Primitive characters and Gauss sums -- Analytic properties of the zeta function and L-functions -- Primes in arithmetic progressions II -- Explicit formulae -- Conditional estimates -- Zeros -- Oscillations of error terms -- Appendices. A. The Riemann-Stieltjes integral; B. Bernoulli numbers and the Euler-MacLaurin summation formula; C. The gamma function; D. Topics in harmonic analysis Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises Numbers, Prime Multiplikative Zahlentheorie (DE-588)4040699-4 gnd rswk-swf Multiplikative Zahlentheorie (DE-588)4040699-4 s DE-604 Vaughan, Robert Charles Sonstige (DE-588)1057557110 oth Erscheint auch als Druck-Ausgabe 978-1-107-40582-0 Erscheint auch als Druck-Ausgabe 978-0-521-84903-6 Cambridge studies in advanced mathematics 97 (DE-604)BV044781283 97 https://doi.org/10.1017/CBO9780511618314 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Montgomery, Hugh L. 1944- Multiplicative number theory I classical theory Cambridge studies in advanced mathematics Dirichlet series I -- The elementary theory of arithmetic functions -- Principles and first examples of sieve methods -- Primes in arithmetic progressions I -- Dirichlet series II -- The prime number theorem -- Applications of the prime number theorem -- Further discussion of the prime number theorem -- Primitive characters and Gauss sums -- Analytic properties of the zeta function and L-functions -- Primes in arithmetic progressions II -- Explicit formulae -- Conditional estimates -- Zeros -- Oscillations of error terms -- Appendices. A. The Riemann-Stieltjes integral; B. Bernoulli numbers and the Euler-MacLaurin summation formula; C. The gamma function; D. Topics in harmonic analysis Numbers, Prime Multiplikative Zahlentheorie (DE-588)4040699-4 gnd |
| subject_GND | (DE-588)4040699-4 |
| title | Multiplicative number theory I classical theory |
| title_auth | Multiplicative number theory I classical theory |
| title_exact_search | Multiplicative number theory I classical theory |
| title_full | Multiplicative number theory I classical theory Hugh L. Montgomery, Robert C. Vaughn |
| title_fullStr | Multiplicative number theory I classical theory Hugh L. Montgomery, Robert C. Vaughn |
| title_full_unstemmed | Multiplicative number theory I classical theory Hugh L. Montgomery, Robert C. Vaughn |
| title_short | Multiplicative number theory I |
| title_sort | multiplicative number theory i classical theory |
| title_sub | classical theory |
| topic | Numbers, Prime Multiplikative Zahlentheorie (DE-588)4040699-4 gnd |
| topic_facet | Numbers, Prime Multiplikative Zahlentheorie |
| url | https://doi.org/10.1017/CBO9780511618314 |
| volume_link | (DE-604)BV044781283 |
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