Problems in analytic number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Graduate texts in mathematics
206 : Readings in mathematics |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 452 S. 25 cm |
| ISBN: | 0387951431 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV013641748 | ||
| 003 | DE-604 | ||
| 005 | 20050311 | ||
| 007 | t | ||
| 008 | 010306s2001 gw |||| |||| 00||| eng d | ||
| 016 | 7 | |a 960850457 |2 DE-101 | |
| 020 | |a 0387951431 |9 0-387-95143-1 | ||
| 035 | |a (OCoLC)44713013 | ||
| 035 | |a (DE-599)BVBBV013641748 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-355 |a DE-739 |a DE-703 |a DE-824 |a DE-19 |a DE-706 |a DE-634 |a DE-11 |a DE-188 |a DE-29T | ||
| 050 | 0 | |a QA241 | |
| 082 | 0 | |a 512/.73 |2 21 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 100 | 1 | |a Murty, Maruti Ram |d 1953- |e Verfasser |0 (DE-588)120837307 |4 aut | |
| 245 | 1 | 0 | |a Problems in analytic number theory |c M. Ram Murty |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XVI, 452 S. |b 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 206 : Readings in mathematics | |
| 650 | 7 | |a Getaltheorie |2 gtt | |
| 650 | 4 | |a Nombres, Théorie des - Problèmes et exercices | |
| 650 | 7 | |a Problemen |2 gtt | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Analytische Zahlentheorie |0 (DE-588)4001870-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Analytische Zahlentheorie |0 (DE-588)4001870-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Graduate texts in mathematics |v 206 : Readings in mathematics |w (DE-604)BV000000067 |9 206 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009321132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009321132 | ||
Datensatz im Suchindex
| _version_ | 1804128452158160896 |
|---|---|
| adam_text | Contents
Preface vii
Acknowledgments xi
I Problems 1
1 Arithmetic Functions 3
1.1 The Mobius Inversion Formula and Applications . . 4
1.2 Formal Dirichlet Series 7
1.3 Orders of Some Arithmetical Functions 9
1.4 Average Orders of Arithmetical Functions 10
1.5 Supplementary Problems 11
2 Primes in Arithmetic Progressions 17
2.1 Summation Techniques 17
2.2 Characters mod q 22
2.3 Dirichlet s Theorem 24
2.4 Dirichlet s Hyperbola Method 27
2.5 Supplementary Problems 29
xiv Contents
3 The Prime Number Theorem 35
3.1 Chebyshev s Theorem 36
3.2 Nonvanishing of Dirichlet Series on Re(s) = 1 .... 39
3.3 The Ikehara Wiener Theorem 42
3.4 Supplementary Problems 48
4 The Method of Contour Integration 53
4.1 Some Basic Integrals 53
4.2 The Prime Number Theorem 57
4.3 Further Examples 62
4.4 Supplementary Problems 64
5 Functional Equations 69
5.1 Poisson s Summation Formula 69
5.2 The Riemann Zeta Function 72
5.3 Gauss Sums 75
5.4 Dirichlet L functions 76
5.5 Supplementary Problems 79
6 Hadamard Products 85
6.1 Jensen s Theorem 85
6.2 Entire Functions of Order 1 88
6.3 The Gamma Function 91
6.4 Infinite Products for £(s) and £(s, x) 93
6.5 Zero Free Regions for ((s) and L(s,x) 94
6.6 Supplementary Problems 99
7 Explicit Formulas 101
7.1 Counting Zeros 101
7.2 Explicit Formula for ip{x) 104
7.3 Weil s Explicit Formula 107
7.4 Supplementary Problems Ill
8 The Selberg Class 115
8.1 The Phragmen Lindelof Theorem 116
8.2 Basic Properties 118
8.3 Selberg s Conjectures 123
8.4 Supplementary Problems 125
Contents xv
9 Sieve Methods 127
9.1 The Sieve of Eratosthenes 127
9.2 Brun s Elementary Sieve 133
9.3 Selberg s Sieve 138
9.4 Supplementary Problems 143
10 p adic Methods 147
10.1 Ostrowski s Theorem 147
10.2 Hensel s Lemma 155
10.3 p adic Interpolation 159
10.4 The p adic Zeta Function 165
10.5 Supplementary Problems 168
11 Solutions 171
1 Arithmetic Functions 173
1.1 The Mobius Inversion Formula and Applications . . 173
1.2 Formal Dirichlet Series 182
1.3 Orders of Some Arithmetical Functions 186
1.4 Average Orders of Arithmetical Functions 189
1.5 Supplementary Problems 194
2 Primes in Arithmetic Progressions 211
2.1 Characters mod q 211
2.2 Dirichlet s Theorem 220
2.3 Dirichlet s Hyperbola Method 225
2.4 Supplementary Problems 231
3 The Prime Number Theorem 247
3.1 Chebyshev s Theorem 247
3.2 Nonvanishing of Dirichlet Series on Re(s) = 1 .... 254
3.3 The Ikehara Wiener Theorem 262
3.4 Supplementary Problems 266
4 The Method of Contour Integration 279
4.1 Some Basic Integrals 279
4.2 The Prime Number Theorem 285
4.3 Further Examples 288
4.4 Supplementary Problems 291
xvi Contents
5 Functional Equations 303
5.1 Poisson s Summation Formula 303
5.2 The Riemann Zeta Function 306
5.3 Gauss Sums 307
5.4 Dirichlet L functions 309
5.5 Supplementary Problems 312
6 Hadamard Products 331
6.1 Jensen s theorem 331
6.2 The Gamma Function 332
6.3 Infinite Products for £(s) and £{s,x) 343
6.4 Zero Free Regions for ((s) and L(s,x) 348
6.5 Supplementary Problems 353
7 Explicit Formulas 357
7.1 Counting Zeros 357
7.2 Explicit Formula for ip{x) 360
7.3 Supplementary Problems 366
8 The Selberg Class 377
8.1 The Phragmen Lindelof Theorem 377
8.2 Basic Properties 378
8.3 Selberg s Conjectures 385
8.4 Supplementary Problems 390
9 Sieve Methods 397
9.1 The Sieve of Eratosthenes 397
9.2 Brun s Elementary Sieve 404
9.3 Selberg s Sieve 406
9.4 Supplementary Problems 413
10 p adic Methods 423
10.1 Ostrowski s Theorem 423
10.2 Hensel s Lemma 428
10.3 p adic Interpolation 431
10.4 The p adic ( Function 437
10.5 Supplementary Problems 441
References 447
Index 449
|
| any_adam_object | 1 |
| author | Murty, Maruti Ram 1953- |
| author_GND | (DE-588)120837307 |
| author_facet | Murty, Maruti Ram 1953- |
| author_role | aut |
| author_sort | Murty, Maruti Ram 1953- |
| author_variant | m r m mr mrm |
| building | Verbundindex |
| bvnumber | BV013641748 |
| callnumber-first | Q - Science |
| callnumber-label | QA241 |
| callnumber-raw | QA241 |
| callnumber-search | QA241 |
| callnumber-sort | QA 3241 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)44713013 (DE-599)BVBBV013641748 |
| 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 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01694nam a2200433 cb4500</leader><controlfield tag="001">BV013641748</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20050311 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">010306s2001 gw |||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">960850457</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387951431</subfield><subfield code="9">0-387-95143-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)44713013</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013641748</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-29T</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA241</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.73</subfield><subfield code="2">21</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">Murty, Maruti Ram</subfield><subfield code="d">1953-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)120837307</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Problems in analytic number theory</subfield><subfield code="c">M. Ram Murty</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 452 S.</subfield><subfield code="b">25 cm</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">206 : Readings in mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Getaltheorie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nombres, Théorie des - Problèmes et exercices</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Problemen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analytische Zahlentheorie</subfield><subfield code="0">(DE-588)4001870-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analytische Zahlentheorie</subfield><subfield code="0">(DE-588)4001870-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">206 : Readings in mathematics</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">206</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009321132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009321132</subfield></datafield></record></collection> |
| id | DE-604.BV013641748 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:28Z |
| institution | BVB |
| isbn | 0387951431 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009321132 |
| oclc_num | 44713013 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-739 DE-703 DE-824 DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-29T |
| owner_facet | DE-355 DE-BY-UBR DE-739 DE-703 DE-824 DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 DE-29T |
| physical | XVI, 452 S. 25 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Murty, Maruti Ram 1953- Verfasser (DE-588)120837307 aut Problems in analytic number theory M. Ram Murty New York [u.a.] Springer 2001 XVI, 452 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 206 : Readings in mathematics Getaltheorie gtt Nombres, Théorie des - Problèmes et exercices Problemen gtt Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 s DE-604 Graduate texts in mathematics 206 : Readings in mathematics (DE-604)BV000000067 206 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009321132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Murty, Maruti Ram 1953- Problems in analytic number theory Graduate texts in mathematics Getaltheorie gtt Nombres, Théorie des - Problèmes et exercices Problemen gtt Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| subject_GND | (DE-588)4001870-2 |
| title | Problems in analytic number theory |
| title_auth | Problems in analytic number theory |
| title_exact_search | Problems in analytic number theory |
| title_full | Problems in analytic number theory M. Ram Murty |
| title_fullStr | Problems in analytic number theory M. Ram Murty |
| title_full_unstemmed | Problems in analytic number theory M. Ram Murty |
| title_short | Problems in analytic number theory |
| title_sort | problems in analytic number theory |
| topic | Getaltheorie gtt Nombres, Théorie des - Problèmes et exercices Problemen gtt Number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| topic_facet | Getaltheorie Nombres, Théorie des - Problèmes et exercices Problemen Number theory Analytische Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009321132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT murtymarutiram problemsinanalyticnumbertheory |