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• catalog abstract ""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.".
• catalog contributor b11885124.
• catalog contributor b11885125.
• catalog created "2000.".
• catalog date "2000".
• catalog date "2000.".
• catalog dateCopyrighted "2000.".
• catalog description ""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.".
• catalog description "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.".
• catalog description "Includes bibliographical references and index.".
• catalog extent "xiii, 177 p. ;".
• catalog identifier "0387950974 (alk. paper)".
• catalog isPartOf "Graduate texts in mathematics ; 74".
• catalog issued "2000".
• catalog issued "2000.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog subject "512/.7 21".
• catalog subject "Number theory.".
• catalog subject "Numbers, Prime.".
• catalog subject "QA241 .D32 2000".
• catalog tableOfContents "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.".
• catalog title "Multiplicative number theory / Harold Davenport.".
• catalog type "text".