The distribution of prime numbers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Schriftenreihe: | Graduate studies in mathematics
203 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index 1912 |
| Beschreibung: | xii, 356 Seiten Illustrationen |
| ISBN: | 9781470447540 |
Internformat
MARC
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| 653 | 0 | |a Number theory -- Instructional exposition (textbooks, tutorial papers, etc.) | |
| 653 | 0 | |a Number theory -- Multiplicative number theory | |
| 653 | 0 | |a Number theory -- Zeta and $L$-functions: analytic theory | |
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Datensatz im Suchindex
| _version_ | 1804180961118650368 |
|---|---|
| adam_text | Contents Preface vii Notation xi And then there were infinitely many 1 Part 1. First principles Chapter 1. Asymptotic estimates 8 Chapter 2. Combinatorial ways to count primes 27 Chapter 3. The Dirichlet convolution 35 Chapter 4. Dirichlet series 44 Part 2. Methods of complex and harmonic analysis Chapter 5. An explicit formula for counting primes 52 Chapter 6. The Riemann zeta function 62 Chapter 7. The Perron inversion formula 70 Chapter 8. The Prime Number Theorem 84 Chapter 9. Dirichlet characters 95 Chapter 10. Fourier analysis on finite abelian groups 100 Chapter 11. Dirichlet L-functions 110 Chapter 12. The Prime Number Theorem for arithmetic progressions 118 v
Contents VI Part 3. Multiplicative functions and the anatomy of integers Chapter 13. Primes and multiplicative functions 130 Chapter 14. Evolution of sums of multiplicative functions 143 Chapter 15. The distribution of multiplicative functions 157 Chapter 16. Large deviations 164 Part 4. Sieve methods Chapter 17. Twin primes 174 Chapter 18. The axioms of sieve theory 182 Chapter 19. The Fundamental Lemma of Sieve Theory 192 Chapter 20. Applications of sieve methods 206 Chapter 21. Selberg’s sieve 213 Chapter 22. Sieving for zero-free regions 222 Part 5. Bilinear methods Chapter 23. Vinogradov’s method 234 Chapter 24. Ternary arithmetic progressions 250 Chapter 25. Bilinear forms and the large sieve 259 Chapter 26. The Bombieri-Vinogradov theorem 277 Chapter 27. The least prime in an arithmetic progression 287 Part 6. Local aspects of the distribution of primes Chapter 28. Small gaps between primes 300 Chapter 29. Large gaps between primes 317 Chapter 30. Irregularities in the distribution of primes 329 Appendices Appendix A. The Riemann-Stieltjes integral 336 Appendix B. The Fourier and the Mellin transforms 338 Appendix C. The method of moments 341 Bibliography 344 Index 354
|
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| author | Koukoulopoulos, Dimitris 1984- |
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| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)1151427103 (DE-599)KXP1671713389 |
| dewey-full | 512.7/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.7 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:44:04Z |
| institution | BVB |
| isbn | 9781470447540 |
| language | English |
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| physical | xii, 356 Seiten Illustrationen |
| publishDate | 2019 |
| publishDateSearch | 2019 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Koukoulopoulos, Dimitris 1984- Verfasser (DE-588)1203883935 aut The distribution of prime numbers Dimitris Koukoulopoulos Providence, Rhode Island American Mathematical Society [2019] xii, 356 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 203 Includes bibliographical references and index 1912 Verteilung (DE-588)4432264-1 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Primzahltheorie (DE-588)4175715-4 gnd rswk-swf Numbers, Prime Number theory -- Instructional exposition (textbooks, tutorial papers, etc.) Number theory -- Multiplicative number theory Number theory -- Zeta and $L$-functions: analytic theory Zahlentheorie (DE-588)4067277-3 s Verteilung (DE-588)4432264-1 s Primzahltheorie (DE-588)4175715-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-470-45420-3 Graduate studies in mathematics 203 (DE-604)BV009739289 203 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031830155&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koukoulopoulos, Dimitris 1984- The distribution of prime numbers Graduate studies in mathematics Verteilung (DE-588)4432264-1 gnd Zahlentheorie (DE-588)4067277-3 gnd Primzahltheorie (DE-588)4175715-4 gnd |
| subject_GND | (DE-588)4432264-1 (DE-588)4067277-3 (DE-588)4175715-4 |
| title | The distribution of prime numbers |
| title_auth | The distribution of prime numbers |
| title_exact_search | The distribution of prime numbers |
| title_full | The distribution of prime numbers Dimitris Koukoulopoulos |
| title_fullStr | The distribution of prime numbers Dimitris Koukoulopoulos |
| title_full_unstemmed | The distribution of prime numbers Dimitris Koukoulopoulos |
| title_short | The distribution of prime numbers |
| title_sort | the distribution of prime numbers |
| topic | Verteilung (DE-588)4432264-1 gnd Zahlentheorie (DE-588)4067277-3 gnd Primzahltheorie (DE-588)4175715-4 gnd |
| topic_facet | Verteilung Zahlentheorie Primzahltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031830155&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
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