Multiplicative Number Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1980
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Graduate Texts in Mathematics
74 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimulation, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate for L functions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted |
| Beschreibung: | 1 Online-Ressource (XIII, 177 p) |
| ISBN: | 9781475759273 9781475759297 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-5927-3 |
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| 500 | |a Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimulation, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate for L functions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted | ||
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Datensatz im Suchindex
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| author | Davenport, Harold 1907-1969 |
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-5927-3 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042421677 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475759273 9781475759297 |
| issn | 0072-5285 |
| language | English |
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| physical | 1 Online-Ressource (XIII, 177 p) |
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| publishDate | 1980 |
| publishDateSearch | 1980 |
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| publisher | Springer New York |
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| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Davenport, Harold 1907-1969 Verfasser (DE-588)117709360 aut Multiplicative Number Theory by Harold Davenport Second Edition New York, NY Springer New York 1980 1 Online-Ressource (XIII, 177 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 74 0072-5285 Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimulation, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate for L functions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted Mathematics Number theory Number Theory Mathematik Primzahl (DE-588)4047263-2 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Multiplikative Zahlentheorie (DE-588)4040699-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Multiplikative Zahlentheorie (DE-588)4040699-4 s 2\p DE-604 Primzahl (DE-588)4047263-2 s 3\p DE-604 Graduate Texts in Mathematics 74 (DE-604)BV035421258 74 https://doi.org/10.1007/978-1-4757-5927-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Davenport, Harold 1907-1969 Multiplicative Number Theory Graduate Texts in Mathematics Mathematics Number theory Number Theory Mathematik Primzahl (DE-588)4047263-2 gnd Zahlentheorie (DE-588)4067277-3 gnd Multiplikative Zahlentheorie (DE-588)4040699-4 gnd |
| subject_GND | (DE-588)4047263-2 (DE-588)4067277-3 (DE-588)4040699-4 |
| title | Multiplicative Number Theory |
| title_auth | Multiplicative Number Theory |
| title_exact_search | Multiplicative Number Theory |
| title_full | Multiplicative Number Theory by Harold Davenport |
| title_fullStr | Multiplicative Number Theory by Harold Davenport |
| title_full_unstemmed | Multiplicative Number Theory by Harold Davenport |
| title_short | Multiplicative Number Theory |
| title_sort | multiplicative number theory |
| topic | Mathematics Number theory Number Theory Mathematik Primzahl (DE-588)4047263-2 gnd Zahlentheorie (DE-588)4067277-3 gnd Multiplikative Zahlentheorie (DE-588)4040699-4 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Primzahl Zahlentheorie Multiplikative Zahlentheorie |
| url | https://doi.org/10.1007/978-1-4757-5927-3 |
| volume_link | (DE-604)BV035421258 |
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