The large sieve and its applications: arithmetic geometry, random walks and discrete groups
Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of appl...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2008
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| Series: | Cambridge tracts in mathematics
175 |
| Subjects: | |
| Links: | https://doi.org/10.1017/CBO9780511542947 https://doi.org/10.1017/CBO9780511542947 https://doi.org/10.1017/CBO9780511542947 https://doi.org/10.1017/CBO9780511542947 |
| Summary: | Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups |
| Physical Description: | 1 Online-Ressource (xxi, 293 Seiten) |
| ISBN: | 9780511542947 |
| DOI: | 10.1017/CBO9780511542947 |
Staff View
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| 245 | 1 | 0 | |a The large sieve and its applications |b arithmetic geometry, random walks and discrete groups |c E. Kowalski |
| 246 | 1 | 3 | |a The Large Sieve & its Applications |
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| 505 | 8 | 0 | |g 1 |t Introduction |g 2 |t The principle of the large sieve |g 3 |t Group and conjugacy sieves |g 4 |t Elementary and classical examples |g 5 |t Degrees of representations of finite groups |g 6 |t Probabilistic sieves |g 7 |t Sieving in discrete groups |g 8 |t Sieving for Frobenius over finite fields |g App. A. |t Small sieves |g App. B. |t Local density computations over finite fields |g App. C. |t Representation theory |g App. D. |t Property (T) and Property ([tau]) |g App. E. |t Linear algebraic groups |g App. F. |t Probability theory and random walks |g App. G. |t Sums of multiplicative functions |g App. H. |t Topology |
| 520 | |a Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups | ||
| 650 | 4 | |a Sieves (Mathematics) | |
| 650 | 4 | |a Arithmetical algebraic geometry | |
| 650 | 4 | |a Random walks (Mathematics) | |
| 650 | 4 | |a Discrete groups | |
| 650 | 0 | 7 | |a Siebmethode |0 (DE-588)4181206-2 |2 gnd |9 rswk-swf |
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| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511542947 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
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| author | Kowalski, Emmanuel 1969- |
| author_GND | (DE-588)140530754 |
| author_facet | Kowalski, Emmanuel 1969- |
| author_role | aut |
| author_sort | Kowalski, Emmanuel 1969- |
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| bvnumber | BV043941647 |
| classification_rvk | SK 180 |
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| contents | Introduction The principle of the large sieve Group and conjugacy sieves Elementary and classical examples Degrees of representations of finite groups Probabilistic sieves Sieving in discrete groups Sieving for Frobenius over finite fields Small sieves Local density computations over finite fields Representation theory Property (T) and Property ([tau]) Linear algebraic groups Probability theory and random walks Sums of multiplicative functions Topology |
| ctrlnum | (ZDB-20-CBO)CR9780511542947 (OCoLC)850554058 (DE-599)BVBBV043941647 |
| dewey-full | 512.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.73 |
| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542947 |
| format | Electronic eBook |
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| id | DE-604.BV043941647 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:17Z |
| institution | BVB |
| isbn | 9780511542947 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350617 |
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| physical | 1 Online-Ressource (xxi, 293 Seiten) |
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| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Cambridge University Press |
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| spelling | Kowalski, Emmanuel 1969- Verfasser (DE-588)140530754 aut The large sieve and its applications arithmetic geometry, random walks and discrete groups E. Kowalski The Large Sieve & its Applications Cambridge Cambridge University Press 2008 1 Online-Ressource (xxi, 293 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 175 1 Introduction 2 The principle of the large sieve 3 Group and conjugacy sieves 4 Elementary and classical examples 5 Degrees of representations of finite groups 6 Probabilistic sieves 7 Sieving in discrete groups 8 Sieving for Frobenius over finite fields App. A. Small sieves App. B. Local density computations over finite fields App. C. Representation theory App. D. Property (T) and Property ([tau]) App. E. Linear algebraic groups App. F. Probability theory and random walks App. G. Sums of multiplicative functions App. H. Topology Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups Sieves (Mathematics) Arithmetical algebraic geometry Random walks (Mathematics) Discrete groups Siebmethode (DE-588)4181206-2 gnd rswk-swf Siebmethode (DE-588)4181206-2 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-88851-6 https://doi.org/10.1017/CBO9780511542947 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kowalski, Emmanuel 1969- The large sieve and its applications arithmetic geometry, random walks and discrete groups Introduction The principle of the large sieve Group and conjugacy sieves Elementary and classical examples Degrees of representations of finite groups Probabilistic sieves Sieving in discrete groups Sieving for Frobenius over finite fields Small sieves Local density computations over finite fields Representation theory Property (T) and Property ([tau]) Linear algebraic groups Probability theory and random walks Sums of multiplicative functions Topology Sieves (Mathematics) Arithmetical algebraic geometry Random walks (Mathematics) Discrete groups Siebmethode (DE-588)4181206-2 gnd |
| subject_GND | (DE-588)4181206-2 |
| title | The large sieve and its applications arithmetic geometry, random walks and discrete groups |
| title_alt | The Large Sieve & its Applications Introduction The principle of the large sieve Group and conjugacy sieves Elementary and classical examples Degrees of representations of finite groups Probabilistic sieves Sieving in discrete groups Sieving for Frobenius over finite fields Small sieves Local density computations over finite fields Representation theory Property (T) and Property ([tau]) Linear algebraic groups Probability theory and random walks Sums of multiplicative functions Topology |
| title_auth | The large sieve and its applications arithmetic geometry, random walks and discrete groups |
| title_exact_search | The large sieve and its applications arithmetic geometry, random walks and discrete groups |
| title_full | The large sieve and its applications arithmetic geometry, random walks and discrete groups E. Kowalski |
| title_fullStr | The large sieve and its applications arithmetic geometry, random walks and discrete groups E. Kowalski |
| title_full_unstemmed | The large sieve and its applications arithmetic geometry, random walks and discrete groups E. Kowalski |
| title_short | The large sieve and its applications |
| title_sort | the large sieve and its applications arithmetic geometry random walks and discrete groups |
| title_sub | arithmetic geometry, random walks and discrete groups |
| topic | Sieves (Mathematics) Arithmetical algebraic geometry Random walks (Mathematics) Discrete groups Siebmethode (DE-588)4181206-2 gnd |
| topic_facet | Sieves (Mathematics) Arithmetical algebraic geometry Random walks (Mathematics) Discrete groups Siebmethode |
| url | https://doi.org/10.1017/CBO9780511542947 |
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