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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2004.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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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 | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Number theory. | |
| 650 | 0 | |a Mathematical analysis. | |
| 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 | |
| 700 | 1 | |a Diamond, Harold G., |d 1940- | |
| 776 | 0 | 8 | |i Print version: |a Bateman, P.T. |t Analytic number theory. |d New Jersey : World Scientific, ©2004 |z 9812389385 |z 9812560807 |w (OCoLC)57420268 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=129836 |z Texto completo |
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