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...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2008
|
| Schriftenreihe: | Cambridge tracts in mathematics
175 |
| Schlagwörter: | |
| 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 |
| 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 |
| Umfang: | 1 Online-Ressource (xxi, 293 Seiten) |
| ISBN: | 9780511542947 |
| DOI: | 10.1017/CBO9780511542947 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941647 | ||
| 003 | DE-604 | ||
| 005 | 20190401 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2008 xx o|||| 00||| eng d | ||
| 020 | |a 9780511542947 |c Online |9 978-0-511-54294-7 | ||
| 024 | 7 | |a 10.1017/CBO9780511542947 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511542947 | ||
| 035 | |a (OCoLC)850554058 | ||
| 035 | |a (DE-599)BVBBV043941647 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-355 | ||
| 082 | 0 | |a 512.73 |2 22 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 100 | 1 | |a Kowalski, Emmanuel |d 1969- |e Verfasser |0 (DE-588)140530754 |4 aut | |
| 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 |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2008 | |
| 300 | |a 1 Online-Ressource (xxi, 293 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge tracts in mathematics |v 175 | |
| 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 |
| 689 | 0 | 0 | |a Siebmethode |0 (DE-588)4181206-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-521-88851-6 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511542947 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-029350617 | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511542947 |l DE-12 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511542947 |l DE-92 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511542947 |l DE-355 |p ZDB-20-CBO |q UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1818982568305885184 |
|---|---|
| any_adam_object | |
| author | Kowalski, Emmanuel 1969- |
| author_GND | (DE-588)140530754 |
| author_facet | Kowalski, Emmanuel 1969- |
| author_role | aut |
| author_sort | Kowalski, Emmanuel 1969- |
| author_variant | e k ek |
| building | Verbundindex |
| bvnumber | BV043941647 |
| classification_rvk | SK 180 |
| collection | ZDB-20-CBO |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03544nam a2200505zcb4500</leader><controlfield tag="001">BV043941647</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190401 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2008 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511542947</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-54294-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511542947</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511542947</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)850554058</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941647</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.73</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kowalski, Emmanuel</subfield><subfield code="d">1969-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)140530754</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The large sieve and its applications</subfield><subfield code="b">arithmetic geometry, random walks and discrete groups</subfield><subfield code="c">E. Kowalski</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">The Large Sieve & its Applications</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xxi, 293 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge tracts in mathematics</subfield><subfield code="v">175</subfield></datafield><datafield tag="505" ind1="8" ind2="0"><subfield code="g">1</subfield><subfield code="t">Introduction</subfield><subfield code="g">2</subfield><subfield code="t">The principle of the large sieve</subfield><subfield code="g">3</subfield><subfield code="t">Group and conjugacy sieves</subfield><subfield code="g">4</subfield><subfield code="t">Elementary and classical examples</subfield><subfield code="g">5</subfield><subfield code="t">Degrees of representations of finite groups</subfield><subfield code="g">6</subfield><subfield code="t">Probabilistic sieves</subfield><subfield code="g">7</subfield><subfield code="t">Sieving in discrete groups</subfield><subfield code="g">8</subfield><subfield code="t">Sieving for Frobenius over finite fields</subfield><subfield code="g">App. A.</subfield><subfield code="t">Small sieves</subfield><subfield code="g">App. B.</subfield><subfield code="t">Local density computations over finite fields</subfield><subfield code="g">App. C.</subfield><subfield code="t">Representation theory</subfield><subfield code="g">App. D.</subfield><subfield code="t">Property (T) and Property ([tau])</subfield><subfield code="g">App. E.</subfield><subfield code="t">Linear algebraic groups</subfield><subfield code="g">App. F.</subfield><subfield code="t">Probability theory and random walks</subfield><subfield code="g">App. G.</subfield><subfield code="t">Sums of multiplicative functions</subfield><subfield code="g">App. H.</subfield><subfield code="t">Topology</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sieves (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Arithmetical algebraic geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random walks (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discrete groups</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Siebmethode</subfield><subfield code="0">(DE-588)4181206-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Siebmethode</subfield><subfield code="0">(DE-588)4181206-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-521-88851-6</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511542947</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350617</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511542947</subfield><subfield code="l">DE-12</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511542947</subfield><subfield code="l">DE-92</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511542947</subfield><subfield code="l">DE-355</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UBR Einzelkauf (Lückenergänzung CUP Serien 2018)</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| 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 |
| oclc_num | 850554058 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xxi, 293 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| 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 |
| work_keys_str_mv | AT kowalskiemmanuel thelargesieveanditsapplicationsarithmeticgeometryrandomwalksanddiscretegroups AT kowalskiemmanuel thelargesieveitsapplications |