Analytic number theory :: an introductory course /
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 ("a...
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
New Jersey :
World Scientific,
©2004.
|
Schlagworte: | |
Online-Zugang: | Volltext |
Zusammenfassung: | 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 resource (xiii, 360 pages) : illustrations |
Bibliographie: | Includes bibliographical references (pages 353-354) and indexes. |
ISBN: | 9789812389381 9812389385 9789812560803 9812560807 9812562273 9789812562272 1281872253 9781281872258 9786611872250 6611872256 |
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100 | 1 | |a Bateman, P. T. | |
245 | 1 | 0 | |a Analytic number theory : |b an introductory course / |c Paul T. Bateman, Harold G. Diamond. |
260 | |a New Jersey : |b World Scientific, |c ©2004. | ||
300 | |a 1 online resource (xiii, 360 pages) : |b illustrations | ||
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504 | |a Includes bibliographical references (pages 353-354) and indexes. | ||
505 | 0 | |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 -- 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. | |
588 | 0 | |a Print version record. | |
520 | |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. | ||
546 | |a English. | ||
650 | 0 | |a Number theory. |0 http://id.loc.gov/authorities/subjects/sh85093222 | |
650 | 0 | |a Mathematical analysis. |0 http://id.loc.gov/authorities/subjects/sh85082116 | |
650 | 6 | |a Théorie des nombres. | |
650 | 6 | |a Analyse mathématique. | |
650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
650 | 7 | |a Mathematical analysis |2 fast | |
650 | 7 | |a Number theory |2 fast | |
650 | 7 | |a Nombres, Théorie des. |2 rvm | |
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contents | 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. |
ctrlnum | (OCoLC)61482715 |
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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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. 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id | ZDB-4-EBA-ocm61482715 |
illustrated | Illustrated |
indexdate | 2024-11-27T13:15:46Z |
institution | BVB |
isbn | 9789812389381 9812389385 9789812560803 9812560807 9812562273 9789812562272 1281872253 9781281872258 9786611872250 6611872256 |
language | English |
lccn | 2007297756 |
oclc_num | 61482715 |
open_access_boolean | |
owner | MAIN DE-863 DE-BY-FWS |
owner_facet | MAIN DE-863 DE-BY-FWS |
physical | 1 online resource (xiii, 360 pages) : illustrations |
psigel | ZDB-4-EBA |
publishDate | 2004 |
publishDateSearch | 2004 |
publishDateSort | 2004 |
publisher | World Scientific, |
record_format | marc |
spelling | Bateman, P. T. Analytic number theory : an introductory course / Paul T. Bateman, Harold G. Diamond. New Jersey : World Scientific, ©2004. 1 online resource (xiii, 360 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda 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. Print version record. 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. English. Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Théorie des nombres. Analyse mathématique. MATHEMATICS Number Theory. bisacsh Mathematical analysis fast Number theory fast Nombres, Théorie des. rvm Diamond, Harold G., 1940- https://id.oclc.org/worldcat/entity/E39PCjB4TrPWtk8g7XCQfHYbgq http://id.loc.gov/authorities/names/n96044802 has work: Analytic number theory (Text) https://id.oclc.org/worldcat/entity/E39PCGGWRqYwcjfF3YVbpgMkjC https://id.oclc.org/worldcat/ontology/hasWork Print version: Bateman, P.T. Analytic number theory. New Jersey : World Scientific, ©2004 9812389385 9812560807 (OCoLC)57420268 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=129836 Volltext |
spellingShingle | Bateman, P. T. Analytic number theory : an introductory course / 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. Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Théorie des nombres. Analyse mathématique. MATHEMATICS Number Theory. bisacsh Mathematical analysis fast Number theory fast Nombres, Théorie des. rvm |
subject_GND | http://id.loc.gov/authorities/subjects/sh85093222 http://id.loc.gov/authorities/subjects/sh85082116 |
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 | Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Théorie des nombres. Analyse mathématique. MATHEMATICS Number Theory. bisacsh Mathematical analysis fast Number theory fast Nombres, Théorie des. rvm |
topic_facet | Number theory. Mathematical analysis. Théorie des nombres. Analyse mathématique. MATHEMATICS Number Theory. Mathematical analysis Number theory Nombres, Théorie des. |
url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=129836 |
work_keys_str_mv | AT batemanpt analyticnumbertheoryanintroductorycourse AT diamondharoldg analyticnumbertheoryanintroductorycourse |