Ten lectures on the interface between analytic number theory and harmonic analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
1994
|
| Schriftenreihe: | Regional Conference Series in Mathematics
84 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 220 Seiten graph. Darst. |
| ISBN: | 0821807374 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010330294 | ||
| 003 | DE-604 | ||
| 005 | 20200430 | ||
| 007 | t | ||
| 008 | 950807s1994 d||| |||| 10||| eng d | ||
| 020 | |a 0821807374 |9 0-8218-0737-4 | ||
| 035 | |a (OCoLC)30811108 | ||
| 035 | |a (DE-599)BVBBV010330294 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-739 |a DE-355 |a DE-91G |a DE-19 |a DE-11 |a DE-188 |a DE-20 |a DE-384 | ||
| 050 | 0 | |a QA1 | |
| 082 | 0 | |a 512/.73 |2 20 | |
| 082 | 0 | |a 510 |2 20 | |
| 084 | |a SI 195 |0 (DE-625)143098: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a MAT 430f |2 stub | ||
| 084 | |a MAT 107f |2 stub | ||
| 100 | 1 | |a Montgomery, Hugh L. |d 1944- |e Verfasser |0 (DE-588)172262968 |4 aut | |
| 245 | 1 | 0 | |a Ten lectures on the interface between analytic number theory and harmonic analysis |c Hugh L. Montgomery |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1994 | |
| 300 | |a XIII, 220 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Regional Conference Series in Mathematics |v 84 | |
| 650 | 4 | |a Analyse harmonique - Congrès | |
| 650 | 7 | |a Analyse harmonique - Congrès |2 ram | |
| 650 | 7 | |a Analytische getaltheorie |2 gtt | |
| 650 | 7 | |a Harmonische analyse |2 gtt | |
| 650 | 4 | |a Nombres, Théorie des - Congrès | |
| 650 | 7 | |a Nombres, théorie des - Congrès |2 ram | |
| 650 | 4 | |a Harmonic analysis |v Congresses | |
| 650 | 4 | |a Number theory |v Congresses | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analytische Zahlentheorie |0 (DE-588)4001870-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 1990 |z Manhattan Kan. |2 gnd-content | |
| 689 | 0 | 0 | |a Analytische Zahlentheorie |0 (DE-588)4001870-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Regional Conference Series in Mathematics |v 84 |w (DE-604)BV000004346 |9 84 | |
| 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=006875127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006875127 | ||
Datensatz im Suchindex
| _version_ | 1804124750912421888 |
|---|---|
| adam_text | Contents
Preface xi
Notation xili
Chapter 1. Uniform Distribution 1
1. Qualitative theory 1
2. Quantitative relations 3
3. Trigonometric approximation 10
4. Notes 13
References 15
Chapter 2. van der Corput Sets 17
1. Introduction 17
2. Extremal measures 23
3. Relations between a, /?« , ft 25
4. Corollaries 28
5. A sufficient condition 31
6. Intersective sets 34
7. Heilbronn sets 35
8. Notes 37
References 37
Chapter 3. Exponential Sums I:
The Methods of Weyl and van der Corput 39
1. Introduction 39
2. Weyl s method 39
3. van der Corput s method 46
4. Exponent pairs 56
5. Notes 60
References 61
Chapter 4. Exponential Sums II:
Vinogradov s Method 65
1. Introduction 65
2. Vinogradov s Mean Value Theorem 69
3. A bound for Weyl sums 76
vii
viii CONTENTS
4. An alternative derivation 79
5. Notes 81
References 82
Chapter 5. An Introduction to Turan s Method 85
1. Introduction 85
2. Turan s First Main Theorem 86
3. Fabry s Gap Theorem 89
4. Longer ranges of v 91
5. Turan s Second Main Theorem 93
6. Special coefficients bn 97
7. Notes 102
References 105
Chapter 6. Irregularities of Distribution 109
1. Introduction 109
2. Squares 110
3. Disks 111
4. Decay of the Fourier Transform 114
5. Families allowing translation, scaling and rotation 119
6. Notes 120
References 122
Chapter 7. Mean and Large Values
of Dirichlet Polynomials 125
1. Introduction 125
2. Mean values via trigonometric approximation 127
3. Majorant principles 131
4. Review of Elementary Operator Theory 134
5. Mean values via Hilbert s inequality 137
6. Large value estimates 140
7. Notes 143
References 146
Chapter 8. Distribution of Reduced
Residue Classes in Short Intervals 151
1. Introduction 151
2. A probabilistic model 153
3. An approach by Fourier techniques 154
4. The fundamental lemma 156
5. Notes 160
References 161
Chapter 9. Zeros of X functions 163
1. Introduction 163
2. Least Character Non Residues 164
CONTENTS ix
3. Clumps of zeros 168
4. The Deuring Heilbronn Phenomenon 172
5. Notes 176
References 177
Chapter 10. Small Polynomials
with Integral Coefficients 179
1. Introduction 179
2. The Gorskov Wirsing Polynomials 183
3. Notes 188
References 190
Appendix: Some Unsolved Problems 195
1. Uniform Distribution 195
2. van der Corput Sets 196
3. Weyl Sums 196
4. van der Corput s Method 197
5. Turan s Method 197
6. Irregularities of Distribution 198
7. Mean and Large Values of Dirichlet Polynomials 198
8. Reduced Residues in Short Intervals 200
9. Zeros of L Functions 201
10. Small Polynomials with Integral Coefficients 201
11. Character Sums 202
12. Diophantine Approximation 202
13. Metric Diophantine Approximation 204
14. Algebraic Integers 205
15. Trigonometric Polynomials 206
16. Miscellaneous 207
References 210
Index 215
|
| any_adam_object | 1 |
| author | Montgomery, Hugh L. 1944- |
| author_GND | (DE-588)172262968 |
| author_facet | Montgomery, Hugh L. 1944- |
| author_role | aut |
| author_sort | Montgomery, Hugh L. 1944- |
| author_variant | h l m hl hlm |
| building | Verbundindex |
| bvnumber | BV010330294 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 |
| callnumber-search | QA1 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 195 SK 180 SK 450 |
| classification_tum | MAT 430f MAT 107f |
| ctrlnum | (OCoLC)30811108 (DE-599)BVBBV010330294 |
| dewey-full | 512/.73 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.73 510 |
| dewey-search | 512/.73 510 |
| 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>02314nam a2200565 cb4500</leader><controlfield tag="001">BV010330294</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200430 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">950807s1994 d||| |||| 10||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821807374</subfield><subfield code="9">0-8218-0737-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)30811108</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010330294</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="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA1</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.73</subfield><subfield code="2">20</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 195</subfield><subfield code="0">(DE-625)143098:</subfield><subfield code="2">rvk</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="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 430f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 107f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Montgomery, Hugh L.</subfield><subfield code="d">1944-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)172262968</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Ten lectures on the interface between analytic number theory and harmonic analysis</subfield><subfield code="c">Hugh L. Montgomery</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">1994</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 220 Seiten</subfield><subfield code="b">graph. Darst.</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">Regional Conference Series in Mathematics</subfield><subfield code="v">84</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse harmonique - Congrès</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse harmonique - Congrès</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analytische getaltheorie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Harmonische analyse</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nombres, Théorie des - Congrès</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Nombres, théorie des - Congrès</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic analysis</subfield><subfield code="v">Congresses</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield><subfield code="v">Congresses</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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="655" ind1=" " ind2="7"><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="y">1990</subfield><subfield code="z">Manhattan Kan.</subfield><subfield code="2">gnd-content</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="689" ind1="1" ind2="0"><subfield code="a">Harmonische Analyse</subfield><subfield code="0">(DE-588)4023453-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Regional Conference Series in Mathematics</subfield><subfield code="v">84</subfield><subfield code="w">(DE-604)BV000004346</subfield><subfield code="9">84</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=006875127&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:BVB01-006875127</subfield></datafield></record></collection> |
| genre | (DE-588)1071861417 Konferenzschrift 1990 Manhattan Kan. gnd-content |
| genre_facet | Konferenzschrift 1990 Manhattan Kan. |
| id | DE-604.BV010330294 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:38Z |
| institution | BVB |
| isbn | 0821807374 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006875127 |
| oclc_num | 30811108 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-188 DE-20 DE-384 |
| owner_facet | DE-12 DE-739 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-188 DE-20 DE-384 |
| physical | XIII, 220 Seiten graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Regional Conference Series in Mathematics |
| series2 | Regional Conference Series in Mathematics |
| spelling | Montgomery, Hugh L. 1944- Verfasser (DE-588)172262968 aut Ten lectures on the interface between analytic number theory and harmonic analysis Hugh L. Montgomery Providence, RI American Mathematical Society 1994 XIII, 220 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regional Conference Series in Mathematics 84 Analyse harmonique - Congrès Analyse harmonique - Congrès ram Analytische getaltheorie gtt Harmonische analyse gtt Nombres, Théorie des - Congrès Nombres, théorie des - Congrès ram Harmonic analysis Congresses Number theory Congresses Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1990 Manhattan Kan. gnd-content Analytische Zahlentheorie (DE-588)4001870-2 s DE-604 Harmonische Analyse (DE-588)4023453-8 s Regional Conference Series in Mathematics 84 (DE-604)BV000004346 84 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006875127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Montgomery, Hugh L. 1944- Ten lectures on the interface between analytic number theory and harmonic analysis Regional Conference Series in Mathematics Analyse harmonique - Congrès Analyse harmonique - Congrès ram Analytische getaltheorie gtt Harmonische analyse gtt Nombres, Théorie des - Congrès Nombres, théorie des - Congrès ram Harmonic analysis Congresses Number theory Congresses Harmonische Analyse (DE-588)4023453-8 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4001870-2 (DE-588)1071861417 |
| title | Ten lectures on the interface between analytic number theory and harmonic analysis |
| title_auth | Ten lectures on the interface between analytic number theory and harmonic analysis |
| title_exact_search | Ten lectures on the interface between analytic number theory and harmonic analysis |
| title_full | Ten lectures on the interface between analytic number theory and harmonic analysis Hugh L. Montgomery |
| title_fullStr | Ten lectures on the interface between analytic number theory and harmonic analysis Hugh L. Montgomery |
| title_full_unstemmed | Ten lectures on the interface between analytic number theory and harmonic analysis Hugh L. Montgomery |
| title_short | Ten lectures on the interface between analytic number theory and harmonic analysis |
| title_sort | ten lectures on the interface between analytic number theory and harmonic analysis |
| topic | Analyse harmonique - Congrès Analyse harmonique - Congrès ram Analytische getaltheorie gtt Harmonische analyse gtt Nombres, Théorie des - Congrès Nombres, théorie des - Congrès ram Harmonic analysis Congresses Number theory Congresses Harmonische Analyse (DE-588)4023453-8 gnd Analytische Zahlentheorie (DE-588)4001870-2 gnd |
| topic_facet | Analyse harmonique - Congrès Analytische getaltheorie Harmonische analyse Nombres, Théorie des - Congrès Nombres, théorie des - Congrès Harmonic analysis Congresses Number theory Congresses Harmonische Analyse Analytische Zahlentheorie Konferenzschrift 1990 Manhattan Kan. |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006875127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT montgomeryhughl tenlecturesontheinterfacebetweenanalyticnumbertheoryandharmonicanalysis |