Multiplicative number theory /
This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions, the theorem of Siegel, and functional equations of the L-functions and their c...
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| Format: | Book |
| Language: | English |
| Published: |
New York :
Springer,
2000
New York : c2000 New York : [2000] |
| Edition: | 3rd ed. / |
| Series: | Graduate texts in mathematics ;
74 Graduate texts in mathematics 74 Graduate texts in mathematics ; 74 Graduate texts in mathematics 74 |
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| 100 | 1 | |a Davenport, Harold, |d 1907- | |
| 100 | 1 | |a Davenport, Harold, |d 1907-1969 |1 http://viaf.org/viaf/108168988 | |
| 100 | 1 | |a Davenport, Harold, |d 1907-1969 | |
| 245 | 1 | 0 | |a Multiplicative number theory / |c Harold Davenport |
| 250 | |a 3rd ed. / |b rev. by Hugh 1. Montgomery | ||
| 250 | |a 3rd ed. / |b rev. by Hugh L. Montgomery | ||
| 250 | |a 3rd ed. / |b revised by Hugh L. Montgomery | ||
| 250 | |a Third edition / |b revised by Hugh L. Montgomery | ||
| 260 | |a New York : |b Springer, |c 2000 | ||
| 260 | |a New York : |b Springer, |c c2000 | ||
| 264 | 1 | |a New York : |b Springer, |c [2000] | |
| 264 | 4 | |c ©2000 | |
| 300 | |a xiii, 177 p. ; |c 24 cm | ||
| 300 | |a xiii, 177 p. ; |c 25 cm | ||
| 300 | |a xiii, 177 pages ; |c 25 cm | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 440 | 0 | |a Graduate texts in mathematics ; |v 74 | |
| 440 | 0 | |a Graduate texts in mathematics |v 74 | |
| 490 | 1 | |a Graduate texts in mathematics ; |v 74 | |
| 504 | |a Includes bibliographical references (p. xi) and index | ||
| 504 | |a Includes bibliographical references and index | ||
| 505 | 0 | |a 1. Primes in Arithmetic Progression -- 2. Gauss' Sum -- 3. Cyclotomy -- 4. Primes in Arithmetic Progression: The General Modulus -- 5. Primitive Characters -- 6. Dirichlet's Class Number Formula -- 7. The Distribution of the Primes -- 8. Riemann's Memoir -- 9. The Functional Equation of the L Functions -- 10. Properties of the [Gamma] Function -- 11. Integral Functions of Order 1 -- 12. The Infinite Products for [zeta](s) and [zeta](s, [chi]) -- 13. A Zero-Free Region for [zeta](s) -- 14. Zero-Free Regions for L(s, [chi]) -- 15. The Number N(T) -- 16. The Number N(T, [chi]) -- 17. The Explicit Formula for [psi](x) -- 18. The Prime Number Theorem -- 19. The Explicit Formula for [psi](x, [chi]) -- 20. The Prime Number Theorem for Arithmetic Progressions (I) -- 21. Siegel's Theorem -- 22. The Prime Number Theorem for Arithmetic Progressions (II) -- 23. The Polya-Vinogradov Inequality -- 24. Further Prime Number Sums -- 25. An Exponential Sum Formed with Primes -- 26. Sums of Three Primes -- 27. The Large Sieve -- 28. Bombieri's Theorem -- 29. An Average Result -- 30. References to Other Work | |
| 505 | 0 | 0 | |g 1 |t Primes in Arithmetic Progression -- |g 2. |t Gauss' Sum -- |g 3. |t Cyclotomy -- |g 4. |t Primes in Arithmetic Progression: The General Modulus -- |g 5. |t Primitive Characters -- |g 6. |t Dirichlet's Class Number Formula -- |g 7. |t The Distribution of the Primes -- |g 8. |t Riemann's Memoir -- |g 9. |t The Functional Equation of the L Functions -- |g 10. |t Properties of the [Gamma] Function -- |g 11. |t Integral Functions of Order 1 -- |g 12. |t The Infinite Products for [zeta](s) and [zeta](s, [chi]) -- |g 13. |t A Zero-Free Region for [zeta](s) -- |g 14. |t Zero-Free Regions for L(s, [chi]) -- |g 15. |t The Number N(T) -- |g 16. |t The Number N(T, [chi]) -- |g 17. |t The Explicit Formula for [psi](x) -- |g 18. |t The Prime Number Theorem -- |g 19. |t The Explicit Formula for [psi](x, [chi]) -- |g 20. |t The Prime Number Theorem for Arithmetic Progressions (I) -- |g 21. |t Siegel's Theorem -- |g 22. |t The Prime Number Theorem for Arithmetic Progressions (II) -- |g 23. |t The Polya-Vinogradov Inequality -- |g 24. |t Further Prime Number Sums -- |g 25. |t An Exponential Sum Formed with Primes -- |g 26. |t Sums of Three Primes -- |g 27. |t The Large Sieve -- |g 28. |t Bombieri's Theorem -- |g 29. |t An Average Result -- |g 30. |t References to Other Work. |
| 505 | 0 | 0 | |g 1 |t Primes in Arithmetic Progression -- |g 2. |t Gauss' Sum -- |g 3. |t Cyclotomy -- |g 4. |t Primes in Arithmetic Progression: The General Modulus -- |g 5. |t Primitive Characters -- |g 6. |t Dirichlet's Class Number Formula -- |g 7. |t The Distribution of the Primes -- |g 8. |t Riemann's Memoir -- |g 9. |t The Functional Equation of the L Functions -- |g 10. |t Properties of the [Gamma] Function -- |g 11. |t Integral Functions of Order 1 -- |g 12. |t The Infinite Products for [zeta](s) and [zeta](s, [chi]) -- |g 13. |t A Zero-Free Region for [zeta](s) -- |g 14. |t Zero-Free Regions for L(s, [chi]) -- |g 15. |t The Number N(T) -- |g 16. |t The Number N(T, [chi]) -- |g 17. |t The Explicit Formula for [psi](x) -- |g 18. |t The Prime Number Theorem -- |g 19. |t The Explicit Formula for [psi](x, [chi]) -- |g 20. |t The Prime Number Theorem for Arithmetic Progressions (I) -- |g 21. |t Siegel's Theorem -- |g 22. |t The Prime Number Theorem for Arithmetic Progressions (II) -- |g 23. |t The Polya-Vinogradov Inequality -- |g 24. |t Further Prime Number Sums -- |g 25. |t An Exponential Sum Formed with Primes -- |g 26. |t Sums of Three Primes -- |g 27. |t The Large Sieve -- |g 28. |t Bombieri's Theorem -- |g 29. |t An Average Result -- |g 30. |t References to Other Work. |
| 520 | |a This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions, the theorem of Siegel, and functional equations of the L-functions and their consequences for the distribution of prime numbers. In addition, a simplified, improved version of the large sieve method is presented. The 3rd edition includes a large number of revisions and corrections as well as a new section with references to more recent work in the field | ||
| 520 | 1 | |a "This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetic progressions, the theorem of Siegel, and functional equations of the L-functions and their consequences for the distribution of prime numbers. In addition, a simplified, improved version of the large sieve method is presented. The third edition includes a large number of revisions and corrections as well as a new section with references to more recent work in the field."--BOOK JACKET | |
| 520 | 1 | |a "This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetic progressions, the theorem of Siegel, and functional equations of the L-functions and their consequences for the distribution of prime numbers. In addition, a simplified, improved version of the large sieve method is presented. The third edition includes a large number of revisions and corrections as well as a new section with references to more recent work in the field."--Jacket | |
| 596 | |a 4 | ||
| 650 | 0 | |a Number theory | |
| 650 | 0 | |a Numbers, Prime | |
| 650 | 6 | |a Nombres premiers | |
| 650 | 6 | |a Nombres, Théorie des | |
| 650 | 6 | |a Nombres, Théorie des | |
| 650 | 7 | |a Number theory |2 fast | |
| 650 | 7 | |a Numbers, Prime |2 fast | |
| 650 | 0 | 7 | |a Multiplikative Zahlentheorie |2 swd |
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| 700 | 1 | |a Montgomery, Hugh L |0 http://viaf.org/viaf/41903675 | |
| 700 | 1 | |a Montgomery, Hugh L |1 http://viaf.org/viaf/41903675 | |
| 700 | 1 | |a Montgomery, Hugh L | |
| 830 | 0 | |a Graduate texts in mathematics ; |v 74 | |
| 830 | 0 | |a Graduate texts in mathematics |v 74 | |
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