Analytic methods for Diophantine equations and Diophantine inequalities:
Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequali...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2005
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| Schriftenreihe: | Cambridge mathematical library
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xx, 140 pages) |
| ISBN: | 9780511542893 |
| DOI: | 10.1017/CBO9780511542893 |
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| 245 | 1 | 0 | |a Analytic methods for Diophantine equations and Diophantine inequalities |c H. Davenport |
| 246 | 1 | 3 | |a Analytic Methods for Diophantine Equations & Diophantine Inequalities |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2005 | |
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| 490 | 0 | |a Cambridge mathematical library | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | 0 | |t Waring's problem |r R. C. Vaughan |t Forms in many variables |r D. R. Heath-Brown |t Diophantine inequalities |r D. E. Freeman |g 1 |t Introduction |g 2 |t Waring's problem : history |g 3 |t Weyl's inequality and Hua's inequality |g 4 |t Waring's problem : the asymptotic formula |g 5 |t Waring's problem : the singular series |g 6 |t singular series continued |g 7 |t equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = N |g 8 |t equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 |g 9 |t Waring's problem : the number G(k) |g 10 |t equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 again |g 11 |t General homogeneous equations : Birch's theorem |g 12 |t geometry of numbers |g 13 |t Cubic forms |g 14 |t Cubic forms : bilinear equations |g 15 |t Cubic forms : minor arcs and major arcs |g 16 |t Cubic forms : the singular integral |g 17 |t Cubic forms : the singular series |g 18 |t Cubic forms : the p-adic problem |g 19 |t Homogeneous equations of higher degree |g 20 |t Diophantine inequality |
| 520 | |a Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added | ||
| 650 | 4 | |a Diophantine analysis | |
| 650 | 4 | |a Diophantine equations | |
| 700 | 1 | |a Browning, Tim |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804176883671105536 |
|---|---|
| any_adam_object | |
| author | Davenport, Harold 1907-1969 |
| author_GND | (DE-588)117709360 |
| author_additional | R. C. Vaughan D. R. Heath-Brown D. E. Freeman |
| author_facet | Davenport, Harold 1907-1969 |
| author_role | aut |
| author_sort | Davenport, Harold 1907-1969 |
| author_variant | h d hd |
| building | Verbundindex |
| bvnumber | BV043941645 |
| classification_rvk | SK 180 |
| collection | ZDB-20-CBO |
| contents | Waring's problem Forms in many variables Diophantine inequalities Introduction Waring's problem : history Weyl's inequality and Hua's inequality Waring's problem : the asymptotic formula Waring's problem : the singular series singular series continued equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = N equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 Waring's problem : the number G(k) equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 again General homogeneous equations : Birch's theorem geometry of numbers Cubic forms Cubic forms : bilinear equations Cubic forms : minor arcs and major arcs Cubic forms : the singular integral Cubic forms : the singular series Cubic forms : the p-adic problem Homogeneous equations of higher degree Diophantine inequality |
| ctrlnum | (ZDB-20-CBO)CR9780511542893 (OCoLC)967679385 (DE-599)BVBBV043941645 |
| dewey-full | 512.7/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542893 |
| format | Electronic eBook |
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| id | DE-604.BV043941645 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511542893 |
| language | English |
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| physical | 1 online resource (xx, 140 pages) |
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| spelling | Davenport, Harold 1907-1969 Verfasser (DE-588)117709360 aut Analytic methods for Diophantine equations and Diophantine inequalities H. Davenport Analytic Methods for Diophantine Equations & Diophantine Inequalities Cambridge Cambridge University Press 2005 1 online resource (xx, 140 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge mathematical library Title from publisher's bibliographic system (viewed on 05 Oct 2015) Waring's problem R. C. Vaughan Forms in many variables D. R. Heath-Brown Diophantine inequalities D. E. Freeman 1 Introduction 2 Waring's problem : history 3 Weyl's inequality and Hua's inequality 4 Waring's problem : the asymptotic formula 5 Waring's problem : the singular series 6 singular series continued 7 equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = N 8 equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 9 Waring's problem : the number G(k) 10 equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 again 11 General homogeneous equations : Birch's theorem 12 geometry of numbers 13 Cubic forms 14 Cubic forms : bilinear equations 15 Cubic forms : minor arcs and major arcs 16 Cubic forms : the singular integral 17 Cubic forms : the singular series 18 Cubic forms : the p-adic problem 19 Homogeneous equations of higher degree 20 Diophantine inequality Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added Diophantine analysis Diophantine equations Browning, Tim Sonstige oth Erscheint auch als Druckausgabe 978-0-521-60583-0 https://doi.org/10.1017/CBO9780511542893 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Davenport, Harold 1907-1969 Analytic methods for Diophantine equations and Diophantine inequalities Waring's problem Forms in many variables Diophantine inequalities Introduction Waring's problem : history Weyl's inequality and Hua's inequality Waring's problem : the asymptotic formula Waring's problem : the singular series singular series continued equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = N equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 Waring's problem : the number G(k) equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 again General homogeneous equations : Birch's theorem geometry of numbers Cubic forms Cubic forms : bilinear equations Cubic forms : minor arcs and major arcs Cubic forms : the singular integral Cubic forms : the singular series Cubic forms : the p-adic problem Homogeneous equations of higher degree Diophantine inequality Diophantine analysis Diophantine equations |
| title | Analytic methods for Diophantine equations and Diophantine inequalities |
| title_alt | Analytic Methods for Diophantine Equations & Diophantine Inequalities Waring's problem Forms in many variables Diophantine inequalities Introduction Waring's problem : history Weyl's inequality and Hua's inequality Waring's problem : the asymptotic formula Waring's problem : the singular series singular series continued equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = N equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 Waring's problem : the number G(k) equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 again General homogeneous equations : Birch's theorem geometry of numbers Cubic forms Cubic forms : bilinear equations Cubic forms : minor arcs and major arcs Cubic forms : the singular integral Cubic forms : the singular series Cubic forms : the p-adic problem Homogeneous equations of higher degree Diophantine inequality |
| title_auth | Analytic methods for Diophantine equations and Diophantine inequalities |
| title_exact_search | Analytic methods for Diophantine equations and Diophantine inequalities |
| title_full | Analytic methods for Diophantine equations and Diophantine inequalities H. Davenport |
| title_fullStr | Analytic methods for Diophantine equations and Diophantine inequalities H. Davenport |
| title_full_unstemmed | Analytic methods for Diophantine equations and Diophantine inequalities H. Davenport |
| title_short | Analytic methods for Diophantine equations and Diophantine inequalities |
| title_sort | analytic methods for diophantine equations and diophantine inequalities |
| topic | Diophantine analysis Diophantine equations |
| topic_facet | Diophantine analysis Diophantine equations |
| url | https://doi.org/10.1017/CBO9780511542893 |
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