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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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
©2008.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
175. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xxi, 293 pages :) |
| Bibliographie: | Includes bibliographical references (pages 283-288) and index. |
| ISBN: | 9780521888516 0521888514 9780511400919 0511400918 9780511397295 0511397291 0511398069 9780511398063 9780511542947 0511542941 0511396562 9780511396564 1107187397 9781107187399 1281383848 9781281383846 9786611383848 6611383840 0511398875 9780511398872 |
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| 245 | 1 | 4 | |a The large sieve and its applications : |b arithmetic geometry, random walks and discrete groups / |c E. Kowalski. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c ©2008. | ||
| 300 | |a 1 online resource (xxi, 293 pages :) | ||
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| 490 | 1 | |a Cambridge tracts in mathematics ; |v 175 | |
| 504 | |a Includes bibliographical references (pages 283-288) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 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. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Sieves (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85122374 | |
| 650 | 0 | |a Arithmetical algebraic geometry. |0 http://id.loc.gov/authorities/subjects/sh87002041 | |
| 650 | 0 | |a Random walks (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85111357 | |
| 650 | 0 | |a Discrete groups. |0 http://id.loc.gov/authorities/subjects/sh85038369 | |
| 650 | 6 | |a Cribles (Mathématiques) | |
| 650 | 6 | |a Géométrie algébrique arithmétique. | |
| 650 | 6 | |a Marches aléatoires (Mathématiques) | |
| 650 | 6 | |a Groupes discrets. | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 650 | 7 | |a Arithmetical algebraic geometry |2 fast | |
| 650 | 7 | |a Discrete groups |2 fast | |
| 650 | 7 | |a Random walks (Mathematics) |2 fast | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn316492258 |
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| _version_ | 1813903336577957889 |
| adam_text | |
| any_adam_object | |
| author | Kowalski, Emmanuel, 1969- |
| author_GND | http://id.loc.gov/authorities/names/n2004002624 |
| author_facet | Kowalski, Emmanuel, 1969- |
| author_role | |
| author_sort | Kowalski, Emmanuel, 1969- |
| author_variant | e k ek |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA242 |
| callnumber-raw | QA242.5 .K69 2008 |
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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 | (OCoLC)316492258 |
| dewey-full | 512.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.72 |
| dewey-search | 512.72 |
| dewey-sort | 3512.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| genre_facet | Electronic book. Electronic books. |
| id | ZDB-4-EBA-ocn316492258 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:17:04Z |
| institution | BVB |
| isbn | 9780521888516 0521888514 9780511400919 0511400918 9780511397295 0511397291 0511398069 9780511398063 9780511542947 0511542941 0511396562 9780511396564 1107187397 9781107187399 1281383848 9781281383846 9786611383848 6611383840 0511398875 9780511398872 |
| language | English |
| oclc_num | 316492258 |
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| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xxi, 293 pages :) |
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| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge University Press, |
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| series | Cambridge tracts in mathematics ; |
| series2 | Cambridge tracts in mathematics ; |
| spelling | Kowalski, Emmanuel, 1969- https://id.oclc.org/worldcat/entity/E39PBJbGVCwRb64jfbWXQrqxXd http://id.loc.gov/authorities/names/n2004002624 The large sieve and its applications : arithmetic geometry, random walks and discrete groups / E. Kowalski. Cambridge ; New York : Cambridge University Press, ©2008. 1 online resource (xxi, 293 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Cambridge tracts in mathematics ; 175 Includes bibliographical references (pages 283-288) and index. Print version record. 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. English. Sieves (Mathematics) http://id.loc.gov/authorities/subjects/sh85122374 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Discrete groups. http://id.loc.gov/authorities/subjects/sh85038369 Cribles (Mathématiques) Géométrie algébrique arithmétique. Marches aléatoires (Mathématiques) Groupes discrets. MATHEMATICS Number Theory. bisacsh Arithmetical algebraic geometry fast Discrete groups fast Random walks (Mathematics) fast Sieves (Mathematics) fast Electronic book. Electronic books. has work: The large sieve and its applications (Text) https://id.oclc.org/worldcat/entity/E39PCG7gxG8kx4wpRbbP3rcGxP https://id.oclc.org/worldcat/ontology/hasWork Kowalski, Emmanuel, 1969- Large sieve and its applications. Cambridge, UK ; New York : Cambridge University Press, 2008 9780521888516 (DLC) 2008300417 (OCoLC)221147538 Cambridge tracts in mathematics ; 175. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=228164 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=228164 Volltext |
| spellingShingle | Kowalski, Emmanuel, 1969- The large sieve and its applications : arithmetic geometry, random walks and discrete groups / Cambridge tracts in mathematics ; 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) http://id.loc.gov/authorities/subjects/sh85122374 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Discrete groups. http://id.loc.gov/authorities/subjects/sh85038369 Cribles (Mathématiques) Géométrie algébrique arithmétique. Marches aléatoires (Mathématiques) Groupes discrets. MATHEMATICS Number Theory. bisacsh Arithmetical algebraic geometry fast Discrete groups fast Random walks (Mathematics) fast Sieves (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85122374 http://id.loc.gov/authorities/subjects/sh87002041 http://id.loc.gov/authorities/subjects/sh85111357 http://id.loc.gov/authorities/subjects/sh85038369 |
| title | The large sieve and its applications : arithmetic geometry, random walks and discrete groups / |
| title_alt | 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 | large sieve and its applications arithmetic geometry random walks and discrete groups |
| title_sub | arithmetic geometry, random walks and discrete groups / |
| topic | Sieves (Mathematics) http://id.loc.gov/authorities/subjects/sh85122374 Arithmetical algebraic geometry. http://id.loc.gov/authorities/subjects/sh87002041 Random walks (Mathematics) http://id.loc.gov/authorities/subjects/sh85111357 Discrete groups. http://id.loc.gov/authorities/subjects/sh85038369 Cribles (Mathématiques) Géométrie algébrique arithmétique. Marches aléatoires (Mathématiques) Groupes discrets. MATHEMATICS Number Theory. bisacsh Arithmetical algebraic geometry fast Discrete groups fast Random walks (Mathematics) fast Sieves (Mathematics) fast |
| topic_facet | Sieves (Mathematics) Arithmetical algebraic geometry. Random walks (Mathematics) Discrete groups. Cribles (Mathématiques) Géométrie algébrique arithmétique. Marches aléatoires (Mathématiques) Groupes discrets. MATHEMATICS Number Theory. Arithmetical algebraic geometry Discrete groups Electronic book. Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=228164 |
| work_keys_str_mv | AT kowalskiemmanuel thelargesieveanditsapplicationsarithmeticgeometryrandomwalksanddiscretegroups AT kowalskiemmanuel largesieveanditsapplicationsarithmeticgeometryrandomwalksanddiscretegroups |