Limit theorems for the Riemann zeta-function:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | Mathematics and its applications
352 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 297 S. |
| ISBN: | 0792338243 |
Internformat
MARC
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| 100 | 1 | |a Laurinčikas, Antanas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Limit theorems for the Riemann zeta-function |c by Antanas Laurinčikas |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a XIII, 297 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 352 | |
| 650 | 7 | |a Fonctions zeta |2 ram | |
| 650 | 4 | |a Fonctions zêta | |
| 650 | 4 | |a Série Dirichlet | |
| 650 | 4 | |a Théorie probabiliste nombre | |
| 650 | 4 | |a Théorème limite fonction zeta | |
| 650 | 4 | |a Théorèmes limites (Théorie des probabilités) | |
| 650 | 7 | |a Théorèmes limites (Théorie des probabilités) |2 ram | |
| 650 | 4 | |a Functions, Zeta | |
| 650 | 4 | |a Limit theorems (Probability theory) | |
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| 689 | 0 | 1 | |a Grenzwertsatz |0 (DE-588)4158163-5 |D s |
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Datensatz im Suchindex
| _version_ | 1804125336958402560 |
|---|---|
| adam_text | Contents
Preface xi
Chapter 1. Elements of the Probability Theory 1
1.1. Weak Convergence of Probability Measures 1
1.2. Random Elements 4
1.3. Distribution Functions, Characteristic Functions and other
Transforms 7
1.4. The Haar Measure 11
1.5. Weak Convergence of Probability Measures on the Complex
Plane 12
1.6. Elements of Ergodic Theory 18
1.7. Supports of Random Elements in the Space of Analytic
Functions 20
Notes 25
Chapter 2. Dirichlet Series and Dirichlet Polynomials 26
2.1. Definition and Convergence of Dirichlet Series 26
2.2. Perron s Formula 29
2.3. The Euler Identity 32
2.4. The Bessel Functions 33
2.5. A Limit Theorem for Trigonometric Polynomial 35
2.6. The Besicovitch Spaces 38
2.7. Some Estimates for the Dirichlet Polynomials 48
2.8. Riemann Zeta Function 52
2.9. Dirichlet L Functions 66
2.10. Asymptotics of the Dirichlet Polynomials 72
2.11. Inequality of Large Sieve Type 81
Notes 86
viii CONTENTS
Chapter 3. Limit Theorems for the Modulus of the Riemann Zeta Function 87
3.1. Limit Theorem for the Modulus of the Riemann
Zeta Function in the Half Plane a /2 87
3.2. Moments of the Riemann Zeta Function near the Critical
Line 93
3.3. Necessity of the Power Norming 109
3.4. Limit Theorem for the Modulus of the Riemann
Zeta Function near the Critical Line 112
3.5. Limit Theorem for the Modulus of the Riemann
Zeta Function on the Critical Line 118
3.6. Limit Theorem for the Modulus of the Argument of the
Riemann Zeta Function 136
Notes 146
Chapter 4. Limit Theorems for the Riemann Zeta Function on the Complex
Plane 149
4.1. Limit Theorems for the Riemann Zeta Function on the
Half Plane a 1/2 149
4.2. Limit Theorem on the Complex Plane for the Riemann
Zeta Function near and on the Critical Line 157
Notes 174
Chapter 5. Limit Theorems for the Riemann Zeta Function in the Space of
Analytic Functions 179
5.1. Definition of an #(D) valued Random Element 179
5.2. Limit Theorems for the Dirichlet Polynomials in the Space
of Analytic Functions 184
5.3. Application of the Ergodic Theory 186
5.4. Approximation by Mean of the Function £(s) by Absolutely
Convergent Series 190
5.5. Limit Theorem in the Space of Analytic Functions for the
Absolutely Convergent Series 194
5.6. Proof of Theorem 1.8 198
Notes 202
Chapter 6. Universality Theorem for the Riemann Zeta Function 203
6.1. Some Results on the Hilbert Spaces 203
CONTENTS ix
6.2. The Space H2 on the Unit Disk 212
6.3. The Space H2 over General Domains 214
6.4. Elements of the Theory of Entire Functions 218
6.5. The Universality Theorem 224
6.6. Functional Independence of the Riemann Zeta Function .. 232
Notes 234
Chapter 7. Limit Theorem for the Riemann Zeta Function in the Space of
Continuous Functions 237
7.1. Limit Theorem for the Sum ST(s) in the Space C(R) 238
7.2. Limit Theorem for the Riemann Zeta Function near the
Critical Line in the Space of Continuous Functions 246
Notes 250
Chapter 8. Limit Theorems for Dirichlet L Functions 251
8.1. Limit Theorem for the Dirichlet L Functions on the
Half Plane a 1/2 251
8.2. Limit Theorem for the Dirichlet L Functions near the
Critical Line 254
8.3. Limit Theorem for the Dirichlet L functions with an
Increasing Modulus 261
Notes 274
Chapter 9. Limit Theorem for the Dirichlet Series with Multiplicative
Coefficients 276
9.1. Limit Theorem for Z(s) 276
9.2. The Universality of the Function Z(s) 281
9.3. Functional Independence of the Function Z(s) 283
Notes 284
References 286
Notation 291
Subject Index 295
|
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| id | DE-604.BV010850574 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:59:57Z |
| institution | BVB |
| isbn | 0792338243 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007252798 |
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| physical | XIII, 297 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Laurinčikas, Antanas Verfasser aut Limit theorems for the Riemann zeta-function by Antanas Laurinčikas Dordrecht [u.a.] Kluwer 1996 XIII, 297 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 352 Fonctions zeta ram Fonctions zêta Série Dirichlet Théorie probabiliste nombre Théorème limite fonction zeta Théorèmes limites (Théorie des probabilités) Théorèmes limites (Théorie des probabilités) ram Functions, Zeta Limit theorems (Probability theory) Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Riemannsche Zetafunktion (DE-588)4308419-9 gnd rswk-swf Riemannsche Zetafunktion (DE-588)4308419-9 s Grenzwertsatz (DE-588)4158163-5 s DE-604 Mathematics and its applications 352 (DE-604)BV008163334 352 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007252798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Laurinčikas, Antanas Limit theorems for the Riemann zeta-function Mathematics and its applications Fonctions zeta ram Fonctions zêta Série Dirichlet Théorie probabiliste nombre Théorème limite fonction zeta Théorèmes limites (Théorie des probabilités) Théorèmes limites (Théorie des probabilités) ram Functions, Zeta Limit theorems (Probability theory) Grenzwertsatz (DE-588)4158163-5 gnd Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| subject_GND | (DE-588)4158163-5 (DE-588)4308419-9 |
| title | Limit theorems for the Riemann zeta-function |
| title_auth | Limit theorems for the Riemann zeta-function |
| title_exact_search | Limit theorems for the Riemann zeta-function |
| title_full | Limit theorems for the Riemann zeta-function by Antanas Laurinčikas |
| title_fullStr | Limit theorems for the Riemann zeta-function by Antanas Laurinčikas |
| title_full_unstemmed | Limit theorems for the Riemann zeta-function by Antanas Laurinčikas |
| title_short | Limit theorems for the Riemann zeta-function |
| title_sort | limit theorems for the riemann zeta function |
| topic | Fonctions zeta ram Fonctions zêta Série Dirichlet Théorie probabiliste nombre Théorème limite fonction zeta Théorèmes limites (Théorie des probabilités) Théorèmes limites (Théorie des probabilités) ram Functions, Zeta Limit theorems (Probability theory) Grenzwertsatz (DE-588)4158163-5 gnd Riemannsche Zetafunktion (DE-588)4308419-9 gnd |
| topic_facet | Fonctions zeta Fonctions zêta Série Dirichlet Théorie probabiliste nombre Théorème limite fonction zeta Théorèmes limites (Théorie des probabilités) Functions, Zeta Limit theorems (Probability theory) Grenzwertsatz Riemannsche Zetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007252798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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