Analytic number theory: an introductory course
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
©2004
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 353-354) and indexes Cover -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 Three problems -- 1.2 Asymmetric distribution of quadratic residues -- 1.3 The prime number theorem -- 1.4 Density of squarefree integers -- 1.5 The Riemann zeta function -- 1.6 Notes -- Chapter 2 Calculus of Arithmetic Functions -- 2.1 Arithmetic functions and convolution -- 2.2 Inverses -- 2.3 Convergence -- 2.4 Exponential mapping -- 2.4.1 The 1 function as an exponential -- 2.4.2 Powers and roots -- 2.5 Multiplicative functions -- 2.6 Notes -- Chapter 3 Summatory Functions -- 3.1 Generalities -- 3.2 Estimate of Q(x) 6x/2 -- 3.3 Riemann-Stieltjes integrals -- 3.4 Riemann-Stieltjes integrators -- 3.4.1 Convolution of integrators -- 3.4.2 Generalization of results on arithmetic functions -- 3.5 Stability -- 3.6 Dirichlets hyperbola method -- 3.7 Notes -- Chapter 4 The Distribution of Prime Numbers -- 4.1 General remarks -- 4.2 The Chebyshev function -- 4.3 Mertens estimates -- 4.4 Convergent sums over primes -- - 4.5 A lower estimate for Eulers function -- 4.6 Notes -- Chapter 5 An Elementary Proof of the P.N.T. -- 5.1 Selbergs formula -- 5.1.1 Features of Selbergs formula -- 5.2 Transformation of Selbergs formula -- 5.2.1 Calculus for R -- 5.3 Deduction of the P.N.T. -- 5.4 Propositions 8220;equivalent to the P.N.T. -- 5.5 Some consequences of the P.N.T. -- 5.6 Notes -- Chapter 6 Dirichlet Series and Mellin Transforms -- 6.1 The use of transforms -- 6.2 Euler products -- 6.3 Convergence -- 6.3.1 Abscissa of convergence -- 6.3.2 Abscissa of absolute convergence -- 6.4 Uniform convergence -- 6.5 Analyticity -- 6.5.1 Analytic continuation -- 6.5.2 Continuation of zeta -- 6.5.3 Example of analyticity on = -- 6.6 Uniqueness -- 6.6.1 Identifying an arithmetic function -- 6.7 Operational calculus -- 6.8 Landau's oscillation theorem -- 6.9 Notes -- Chapter 7 Inversion Formulas -- 7.1 The use of inversion formulas -- 7.2 The Wiener-Ikehara theorem -- 7.2.1 Example. Counting product representations -- - 7.2.2 An O-estimate -- 7.3 A Wiener-Ikehara proof of the P.N.T. -- 7.4 A generalization of the Wiener-Ikehara theorem -- 7.5 The Perron formula -- 7.6 Proof of the Perron formula -- 7.7 Contour deformation in the Perron formula -- 7.7.1 The Fourier series of the sawtooth function -- 7.7.2 Bounded and uniform convergence -- 7.8 A "smoothed" Perron formula -- 7.9 Example. Estimation of [sigma]T(1₂ * 1₃) -- 7.10 Notes -- Chapter 8 The Riemann Zeta Function -- Chapter 9 Primes in Arithmetic Progressions -- Chapter 10 Applications of characters -- Chapter 11 Oscillation theorems -- Chapter 12 Sieves -- Chapter 13 Application of Sieves -- Appendix A. Results from Analysis and Algebra This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed |
| Beschreibung: | 1 Online-Ressource (xiii, 360 pages) |
| ISBN: | 9789812389381 9789812560803 9789812562272 9812389385 9812560807 9812562273 |
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| 100 | 1 | |a Bateman, P. T. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analytic number theory |b an introductory course |c Paul T. Bateman, Harold G. Diamond |
| 264 | 1 | |a New Jersey |b World Scientific |c ©2004 | |
| 300 | |a 1 Online-Ressource (xiii, 360 pages) | ||
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| 500 | |a Cover -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 Three problems -- 1.2 Asymmetric distribution of quadratic residues -- 1.3 The prime number theorem -- 1.4 Density of squarefree integers -- 1.5 The Riemann zeta function -- 1.6 Notes -- Chapter 2 Calculus of Arithmetic Functions -- 2.1 Arithmetic functions and convolution -- 2.2 Inverses -- 2.3 Convergence -- 2.4 Exponential mapping -- 2.4.1 The 1 function as an exponential -- 2.4.2 Powers and roots -- 2.5 Multiplicative functions -- 2.6 Notes -- Chapter 3 Summatory Functions -- 3.1 Generalities -- 3.2 Estimate of Q(x) 6x/2 -- 3.3 Riemann-Stieltjes integrals -- 3.4 Riemann-Stieltjes integrators -- 3.4.1 Convolution of integrators -- 3.4.2 Generalization of results on arithmetic functions -- 3.5 Stability -- 3.6 Dirichlets hyperbola method -- 3.7 Notes -- Chapter 4 The Distribution of Prime Numbers -- 4.1 General remarks -- 4.2 The Chebyshev function -- 4.3 Mertens estimates -- 4.4 Convergent sums over primes -- | ||
| 500 | |a - 4.5 A lower estimate for Eulers function -- 4.6 Notes -- Chapter 5 An Elementary Proof of the P.N.T. -- 5.1 Selbergs formula -- 5.1.1 Features of Selbergs formula -- 5.2 Transformation of Selbergs formula -- 5.2.1 Calculus for R -- 5.3 Deduction of the P.N.T. -- 5.4 Propositions 8220;equivalent to the P.N.T. -- 5.5 Some consequences of the P.N.T. -- 5.6 Notes -- Chapter 6 Dirichlet Series and Mellin Transforms -- 6.1 The use of transforms -- 6.2 Euler products -- 6.3 Convergence -- 6.3.1 Abscissa of convergence -- 6.3.2 Abscissa of absolute convergence -- 6.4 Uniform convergence -- 6.5 Analyticity -- 6.5.1 Analytic continuation -- 6.5.2 Continuation of zeta -- 6.5.3 Example of analyticity on = -- 6.6 Uniqueness -- 6.6.1 Identifying an arithmetic function -- 6.7 Operational calculus -- 6.8 Landau's oscillation theorem -- 6.9 Notes -- Chapter 7 Inversion Formulas -- 7.1 The use of inversion formulas -- 7.2 The Wiener-Ikehara theorem -- 7.2.1 Example. Counting product representations -- | ||
| 500 | |a - 7.2.2 An O-estimate -- 7.3 A Wiener-Ikehara proof of the P.N.T. -- 7.4 A generalization of the Wiener-Ikehara theorem -- 7.5 The Perron formula -- 7.6 Proof of the Perron formula -- 7.7 Contour deformation in the Perron formula -- 7.7.1 The Fourier series of the sawtooth function -- 7.7.2 Bounded and uniform convergence -- 7.8 A "smoothed" Perron formula -- 7.9 Example. Estimation of [sigma]T(1₂ * 1₃) -- 7.10 Notes -- Chapter 8 The Riemann Zeta Function -- Chapter 9 Primes in Arithmetic Progressions -- Chapter 10 Applications of characters -- Chapter 11 Oscillation theorems -- Chapter 12 Sieves -- Chapter 13 Application of Sieves -- Appendix A. Results from Analysis and Algebra | ||
| 500 | |a This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed | ||
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| 650 | 7 | |a Number theory |2 fast | |
| 650 | 7 | |a Nombres, Théorie des |2 rvm | |
| 650 | 4 | |a Number theory | |
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Datensatz im Suchindex
| _version_ | 1804175475001524224 |
|---|---|
| any_adam_object | |
| author | Bateman, P. T. |
| author_facet | Bateman, P. T. |
| author_role | aut |
| author_sort | Bateman, P. T. |
| author_variant | p t b pt ptb |
| building | Verbundindex |
| bvnumber | BV043082034 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)61482715 (DE-599)BVBBV043082034 |
| dewey-full | 512.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.73 |
| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043082034 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:52Z |
| institution | BVB |
| isbn | 9789812389381 9789812560803 9789812562272 9812389385 9812560807 9812562273 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028506225 |
| oclc_num | 61482715 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xiii, 360 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Bateman, P. T. Verfasser aut Analytic number theory an introductory course Paul T. Bateman, Harold G. Diamond New Jersey World Scientific ©2004 1 Online-Ressource (xiii, 360 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 353-354) and indexes Cover -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 Three problems -- 1.2 Asymmetric distribution of quadratic residues -- 1.3 The prime number theorem -- 1.4 Density of squarefree integers -- 1.5 The Riemann zeta function -- 1.6 Notes -- Chapter 2 Calculus of Arithmetic Functions -- 2.1 Arithmetic functions and convolution -- 2.2 Inverses -- 2.3 Convergence -- 2.4 Exponential mapping -- 2.4.1 The 1 function as an exponential -- 2.4.2 Powers and roots -- 2.5 Multiplicative functions -- 2.6 Notes -- Chapter 3 Summatory Functions -- 3.1 Generalities -- 3.2 Estimate of Q(x) 6x/2 -- 3.3 Riemann-Stieltjes integrals -- 3.4 Riemann-Stieltjes integrators -- 3.4.1 Convolution of integrators -- 3.4.2 Generalization of results on arithmetic functions -- 3.5 Stability -- 3.6 Dirichlets hyperbola method -- 3.7 Notes -- Chapter 4 The Distribution of Prime Numbers -- 4.1 General remarks -- 4.2 The Chebyshev function -- 4.3 Mertens estimates -- 4.4 Convergent sums over primes -- - 4.5 A lower estimate for Eulers function -- 4.6 Notes -- Chapter 5 An Elementary Proof of the P.N.T. -- 5.1 Selbergs formula -- 5.1.1 Features of Selbergs formula -- 5.2 Transformation of Selbergs formula -- 5.2.1 Calculus for R -- 5.3 Deduction of the P.N.T. -- 5.4 Propositions 8220;equivalent to the P.N.T. -- 5.5 Some consequences of the P.N.T. -- 5.6 Notes -- Chapter 6 Dirichlet Series and Mellin Transforms -- 6.1 The use of transforms -- 6.2 Euler products -- 6.3 Convergence -- 6.3.1 Abscissa of convergence -- 6.3.2 Abscissa of absolute convergence -- 6.4 Uniform convergence -- 6.5 Analyticity -- 6.5.1 Analytic continuation -- 6.5.2 Continuation of zeta -- 6.5.3 Example of analyticity on = -- 6.6 Uniqueness -- 6.6.1 Identifying an arithmetic function -- 6.7 Operational calculus -- 6.8 Landau's oscillation theorem -- 6.9 Notes -- Chapter 7 Inversion Formulas -- 7.1 The use of inversion formulas -- 7.2 The Wiener-Ikehara theorem -- 7.2.1 Example. Counting product representations -- - 7.2.2 An O-estimate -- 7.3 A Wiener-Ikehara proof of the P.N.T. -- 7.4 A generalization of the Wiener-Ikehara theorem -- 7.5 The Perron formula -- 7.6 Proof of the Perron formula -- 7.7 Contour deformation in the Perron formula -- 7.7.1 The Fourier series of the sawtooth function -- 7.7.2 Bounded and uniform convergence -- 7.8 A "smoothed" Perron formula -- 7.9 Example. Estimation of [sigma]T(1₂ * 1₃) -- 7.10 Notes -- Chapter 8 The Riemann Zeta Function -- Chapter 9 Primes in Arithmetic Progressions -- Chapter 10 Applications of characters -- Chapter 11 Oscillation theorems -- Chapter 12 Sieves -- Chapter 13 Application of Sieves -- Appendix A. Results from Analysis and Algebra This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed MATHEMATICS / Number Theory bisacsh Mathematical analysis fast Number theory fast Nombres, Théorie des rvm Number theory Mathematical analysis Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 s 1\p DE-604 Diamond, Harold G. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=129836 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bateman, P. T. Analytic number theory an introductory course MATHEMATICS / Number Theory bisacsh Mathematical analysis fast Number theory fast Nombres, Théorie des rvm Number theory Mathematical analysis Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| subject_GND | (DE-588)4001870-2 |
| title | Analytic number theory an introductory course |
| title_auth | Analytic number theory an introductory course |
| title_exact_search | Analytic number theory an introductory course |
| title_full | Analytic number theory an introductory course Paul T. Bateman, Harold G. Diamond |
| title_fullStr | Analytic number theory an introductory course Paul T. Bateman, Harold G. Diamond |
| title_full_unstemmed | Analytic number theory an introductory course Paul T. Bateman, Harold G. Diamond |
| title_short | Analytic number theory |
| title_sort | analytic number theory an introductory course |
| title_sub | an introductory course |
| topic | MATHEMATICS / Number Theory bisacsh Mathematical analysis fast Number theory fast Nombres, Théorie des rvm Number theory Mathematical analysis Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| topic_facet | MATHEMATICS / Number Theory Mathematical analysis Number theory Nombres, Théorie des Analytische Zahlentheorie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=129836 |
| work_keys_str_mv | AT batemanpt analyticnumbertheoryanintroductorycourse AT diamondharoldg analyticnumbertheoryanintroductorycourse |