Number theory arising from finite fields: analytic and probabilistic theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
2001
|
| Series: | Pure and applied mathematics
241 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 404 S. |
| ISBN: | 0824705777 |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS
Preface iii
Introduction 1
1 Additive Arithmetical Semigroups and Axiom A# 5
1.1 Basic Concepts and Examples 5
1.2 The Zeta or Generating Function 17
1.3 Averages and Densities in Simple Cases 25
14 Asymptotic Moments of Specific Functions 32
1.5 Error Estimates for Certain Averages 38
2 Asymptotic Enumeration and More Refined Estimates 49
2.1 Asymptotic Enumeration of Modules and Algebras 49
2.2 Sharper Average and Enumerative Estimates 56
3 Abstract Prime Number Theorems (I) 71
3.1 General Remarks and Preliminary Results 71
3.2 Chebyshev Type Upper Bounds 88
3.3 Mertens Type Asymptotic Estimates and Prime Divisor Functions 97
3.4 Abstract Prime Number Theorems and Zeros of the Generating
Function 114
3.5 Explicit Abstract Prime Number Theorems 120
3.6 A Tauberian Theorem of Bombieri 129
3.7 Elementary Proofs 140
3.8 Two Analytical Examples 150
4 More Applications of Prime Counting 163
4.1 More Properties of Prime Divisor Functions in the Classical Case 163
4.2 Maximum Orders of Magnitude in the Classical Case 180
5 Abstract Prime Number Theorems (II) 189
5.1 A Theorem of Indlekofer Manstavicius Warlimont 189
5.2 The Total Number of Zeros of the Generating Function 194
5.3 The Orders of the Zeros 204
5.4 An Alternative Abstract Prime Number Theorem 211
5.5 Beurling Type Abstract Prime Number Theorems 218
V
vi Contents
6 General Mean Value Theorems 227
6.1 Preliminaries 227
6.2 General Mean Value Theorems 242
6.3 An Analogue of the Halasz Wirsing Theorem 252
6.4 Mean Values of Multiplicative Functions 267
6.5 Mean Values of the Functions A and /i 274
6.6 Mean Value Theorems for Beurling Type Semigroups ... 279
7 Basics of Probabilistic Number Theory for Semigroups 282
7.1 Necessary Results from Theory of Probability 282
7.2 Limit Distribution Functions of Real Valued Additive
Functions 297
7.3 An Analogue of the Turan Kubilius Inequality 303
7.4 A Fundamental Lemma 315
7.5 A Probability Model 329
7.6 Infinitely Divisible Distributions and a Central Limit
Theorem 337
7.7 Rate of Convergence to the Normal Law 351
8 Survey of Some Further Topics 353
8.1 Asymptotics of Factorizations 353
8.2 Direct Factors of Arithmetical Semigroups 359
8.3 Sets of Multiples 361
8.4 Further Properties of Special Sets and Functions 364
8.5 More About Polynomials and Finite Fields 367
8.6 Ramanujan Expansions of Arithmetical Functions 373
8.7 Additive Arithmetical Formations 378
Bibliography 385
Notations 397
Index 401
|
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| id | DE-604.BV013778584 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:51:49Z |
| institution | BVB |
| isbn | 0824705777 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009419277 |
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| physical | VI, 404 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Knopfmacher, John Verfasser aut Number theory arising from finite fields analytic and probabilistic theory John Knopfmacher ; Wen-Bin Zhang New York [u.a.] Dekker 2001 VI, 404 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 241 Analytische Zahlentheorie - Galois-Feld Probabilistische Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Galois-Feld (DE-588)4155896-0 gnd rswk-swf Galois-Feld (DE-588)4155896-0 s Zahlentheorie (DE-588)4067277-3 s DE-604 Zhang, Wen-Bin Verfasser aut Pure and applied mathematics 241 (DE-604)BV000001885 241 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009419277&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Knopfmacher, John Zhang, Wen-Bin Number theory arising from finite fields analytic and probabilistic theory Pure and applied mathematics Analytische Zahlentheorie - Galois-Feld Probabilistische Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd Galois-Feld (DE-588)4155896-0 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4155896-0 |
| title | Number theory arising from finite fields analytic and probabilistic theory |
| title_auth | Number theory arising from finite fields analytic and probabilistic theory |
| title_exact_search | Number theory arising from finite fields analytic and probabilistic theory |
| title_full | Number theory arising from finite fields analytic and probabilistic theory John Knopfmacher ; Wen-Bin Zhang |
| title_fullStr | Number theory arising from finite fields analytic and probabilistic theory John Knopfmacher ; Wen-Bin Zhang |
| title_full_unstemmed | Number theory arising from finite fields analytic and probabilistic theory John Knopfmacher ; Wen-Bin Zhang |
| title_short | Number theory arising from finite fields |
| title_sort | number theory arising from finite fields analytic and probabilistic theory |
| title_sub | analytic and probabilistic theory |
| topic | Analytische Zahlentheorie - Galois-Feld Probabilistische Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd Galois-Feld (DE-588)4155896-0 gnd |
| topic_facet | Analytische Zahlentheorie - Galois-Feld Probabilistische Zahlentheorie Zahlentheorie Galois-Feld |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009419277&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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