Van der Corputʼs method of exponential sums /:
This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professional...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1991.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
126. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem. |
| Beschreibung: | 1 online resource (119 pages) |
| Bibliographie: | Includes bibliographical references (pages 117-119) and index. |
| ISBN: | 9781107361386 1107361389 9780511661976 0511661975 |
Internformat
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| 245 | 1 | 0 | |a Van der Corputʼs method of exponential sums / |c S.W. Graham and G. Kolesnik. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1991. | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 126 | |
| 504 | |a Includes bibliographical references (pages 117-119) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Basic Definitions; 1.2 Historical Overview; 1.3 Two Dimensional Sums; 1.4 The method of Bombieri and Iwaniec; 1.5 Notation; 2 The Simplest Van Der Corput Estimates; 2.1 Estimates Using First and Second Derivatives; 2.2 Some Simple Inequalities; 2.3 The Weyl-van der Corput Inequality; 2.4 Iterating Weyl-Van der Corput; 2.5 Upper Bounds for the Riemann Zeta-function; 2.6 Notes; 3 The Method of Exponent Pairs; 3.1 Introduction; 3.2 Lemmas on Exponential Integrals; 3.3 Heuristic Arguments and Definitions; 3.4 Proof of the A-Process | |
| 505 | 8 | |a 7.2 Preliminaries7.3 The Airy-Hardy Integral; 7.4 Gauss Sums; 7.5 Lemmas on Rational Points; 7.6 Semicubical Powers of Integers; 7.7 Proof of the Theorem; 7.8 Notes; Appendix; Bibliography; Index | |
| 650 | 0 | |a Exponential sums. |0 http://id.loc.gov/authorities/subjects/sh87005567 | |
| 650 | 6 | |a Sommes exponentielles. | |
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| 650 | 1 | 7 | |a Exponentiële sommen. |2 gtt |
| 650 | 7 | |a Sommes exponentielles. |2 ram | |
| 700 | 1 | |a Kolesnik, G. | |
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| adam_text | |
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| author | Graham, S. W. |
| author2 | Kolesnik, G. |
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| contents | Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Basic Definitions; 1.2 Historical Overview; 1.3 Two Dimensional Sums; 1.4 The method of Bombieri and Iwaniec; 1.5 Notation; 2 The Simplest Van Der Corput Estimates; 2.1 Estimates Using First and Second Derivatives; 2.2 Some Simple Inequalities; 2.3 The Weyl-van der Corput Inequality; 2.4 Iterating Weyl-Van der Corput; 2.5 Upper Bounds for the Riemann Zeta-function; 2.6 Notes; 3 The Method of Exponent Pairs; 3.1 Introduction; 3.2 Lemmas on Exponential Integrals; 3.3 Heuristic Arguments and Definitions; 3.4 Proof of the A-Process 7.2 Preliminaries7.3 The Airy-Hardy Integral; 7.4 Gauss Sums; 7.5 Lemmas on Rational Points; 7.6 Semicubical Powers of Integers; 7.7 Proof of the Theorem; 7.8 Notes; Appendix; Bibliography; Index |
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| dewey-full | 512.73 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839304363 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107361386 1107361389 9780511661976 0511661975 |
| language | English |
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| series2 | London Mathematical Society lecture note series ; |
| spelling | Graham, S. W. Van der Corputʼs method of exponential sums / S.W. Graham and G. Kolesnik. Cambridge ; New York : Cambridge University Press, 1991. 1 online resource (119 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 126 Includes bibliographical references (pages 117-119) and index. Print version record. This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem. Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Basic Definitions; 1.2 Historical Overview; 1.3 Two Dimensional Sums; 1.4 The method of Bombieri and Iwaniec; 1.5 Notation; 2 The Simplest Van Der Corput Estimates; 2.1 Estimates Using First and Second Derivatives; 2.2 Some Simple Inequalities; 2.3 The Weyl-van der Corput Inequality; 2.4 Iterating Weyl-Van der Corput; 2.5 Upper Bounds for the Riemann Zeta-function; 2.6 Notes; 3 The Method of Exponent Pairs; 3.1 Introduction; 3.2 Lemmas on Exponential Integrals; 3.3 Heuristic Arguments and Definitions; 3.4 Proof of the A-Process 7.2 Preliminaries7.3 The Airy-Hardy Integral; 7.4 Gauss Sums; 7.5 Lemmas on Rational Points; 7.6 Semicubical Powers of Integers; 7.7 Proof of the Theorem; 7.8 Notes; Appendix; Bibliography; Index Exponential sums. http://id.loc.gov/authorities/subjects/sh87005567 Sommes exponentielles. MATHEMATICS Number Theory. bisacsh Exponential sums fast Exponentialsumme gnd http://d-nb.info/gnd/4201355-0 Schranke Mathematik gnd http://d-nb.info/gnd/4199965-4 Schätztheorie gnd http://d-nb.info/gnd/4121608-8 Exponentiële sommen. gtt Sommes exponentielles. ram Kolesnik, G. has work: Van der corput's method of exponential sums (Text) https://id.oclc.org/worldcat/entity/E39PCXQd4G7bXYCh8R6P89YWym https://id.oclc.org/worldcat/ontology/hasWork Print version: Graham, S.W. Van der Corputʼs method of exponential sums. Cambridge ; New York : Cambridge University Press, 1991 0521339278 (DLC) 91146734 (OCoLC)23068135 London Mathematical Society lecture note series ; 126. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552437 Volltext |
| spellingShingle | Graham, S. W. Van der Corputʼs method of exponential sums / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Basic Definitions; 1.2 Historical Overview; 1.3 Two Dimensional Sums; 1.4 The method of Bombieri and Iwaniec; 1.5 Notation; 2 The Simplest Van Der Corput Estimates; 2.1 Estimates Using First and Second Derivatives; 2.2 Some Simple Inequalities; 2.3 The Weyl-van der Corput Inequality; 2.4 Iterating Weyl-Van der Corput; 2.5 Upper Bounds for the Riemann Zeta-function; 2.6 Notes; 3 The Method of Exponent Pairs; 3.1 Introduction; 3.2 Lemmas on Exponential Integrals; 3.3 Heuristic Arguments and Definitions; 3.4 Proof of the A-Process 7.2 Preliminaries7.3 The Airy-Hardy Integral; 7.4 Gauss Sums; 7.5 Lemmas on Rational Points; 7.6 Semicubical Powers of Integers; 7.7 Proof of the Theorem; 7.8 Notes; Appendix; Bibliography; Index Exponential sums. http://id.loc.gov/authorities/subjects/sh87005567 Sommes exponentielles. MATHEMATICS Number Theory. bisacsh Exponential sums fast Exponentialsumme gnd http://d-nb.info/gnd/4201355-0 Schranke Mathematik gnd http://d-nb.info/gnd/4199965-4 Schätztheorie gnd http://d-nb.info/gnd/4121608-8 Exponentiële sommen. gtt Sommes exponentielles. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh87005567 http://d-nb.info/gnd/4201355-0 http://d-nb.info/gnd/4199965-4 http://d-nb.info/gnd/4121608-8 |
| title | Van der Corputʼs method of exponential sums / |
| title_auth | Van der Corputʼs method of exponential sums / |
| title_exact_search | Van der Corputʼs method of exponential sums / |
| title_full | Van der Corputʼs method of exponential sums / S.W. Graham and G. Kolesnik. |
| title_fullStr | Van der Corputʼs method of exponential sums / S.W. Graham and G. Kolesnik. |
| title_full_unstemmed | Van der Corputʼs method of exponential sums / S.W. Graham and G. Kolesnik. |
| title_short | Van der Corputʼs method of exponential sums / |
| title_sort | van der corputʼs method of exponential sums |
| topic | Exponential sums. http://id.loc.gov/authorities/subjects/sh87005567 Sommes exponentielles. MATHEMATICS Number Theory. bisacsh Exponential sums fast Exponentialsumme gnd http://d-nb.info/gnd/4201355-0 Schranke Mathematik gnd http://d-nb.info/gnd/4199965-4 Schätztheorie gnd http://d-nb.info/gnd/4121608-8 Exponentiële sommen. gtt Sommes exponentielles. ram |
| topic_facet | Exponential sums. Sommes exponentielles. MATHEMATICS Number Theory. Exponential sums Exponentialsumme Schranke Mathematik Schätztheorie Exponentiële sommen. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552437 |
| work_keys_str_mv | AT grahamsw vandercorputʼsmethodofexponentialsums AT kolesnikg vandercorputʼsmethodofexponentialsums |