Number theory and its applications:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2013
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XIII, 194 S. |
| ISBN: | 9789814425636 |
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MARC
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| 245 | 1 | 0 | |a Number theory and its applications |c Fuhuo Li ; Nianliang Wang ; Shigeru Kanemitsu |
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Record in the Search Index
| _version_ | 1804152355884630016 |
|---|---|
| adam_text | Contents
Preface vii
1. Elements of algebra 1
1.1 Preliminaries........................................... 1
1.2 Elements of group theory ................................ 8
1.3 Homomorphisms......................................... . 11
1.4 Quotient groups ........................................ 14
1.5 Rings and fields........................................ 19
1.6 Applications to elementary number
theory.................................................. 31
1.7 Chinese remainder theorem............................... 32
1.8 Applications of the gcd principle....................... 35
1.9 Group actions........................................... 38
1.10 Finite fields........................................... 42
2. Rudiments of algebraic number theory 47
2.1 Galois extensions....................................... 47
2.2 Modules over Dedekind domains.......................... 49
2.3 Algebraic number fields................................. 53
2.4 Completion of a number field............................ 58
2.4.1 Construction of the field........................ 59
2.4.2 Proof of completeness............................ 60
2.5 The quadratic field with the golden
section unit............................................ 61
2.6 Cyclotomic fields....................................... 63
2.7 The dihedral group as a Galois group ................... 68
xi
Number theory and its applications
xii
3. Arithmetical functions and Stieltjes integrals 71
3.1 Arithmetical functions and their
algebraic structure......................................... 71
3.2 Asymptotic formulas for arithmetical
functions .................................................. 81
3.3 Generating functionology.................................... 84
3.4 Hilbert space and number theory............................. 86
3.5 Euler products.............................................. 91
3.6 The hyperbola method....................................... 95
3.7 Applications of Stieltjes integrals......................... 97
3.8 Characters as arithmetic functions......................... 100
4. Quadratic reciprocity through duality 103
4.1 Group characters and duality............................... 103
4.2 Finite Fourier transforms ................................. 109
4.3 Quadratic reciprocity through Dedekind
sums....................................................... 114
4.4 Quadratic reciprocity in algebraic number
fields..................................................... 116
5. Around Dirichlet T-functions 123
5.1 Dirichlet L-functions with primitive
characters................................................. 123
5.2 The quadratic reciprocity.................................. 132
5.3 Lambert series and character sums.......................... 137
5.4 Short interval character sums............................ . 142
5.5 Riemann-Hecke-Bochner correspondence
and character sums......................................... 146
5.6 The t-function ............................................ 148
5.7 Discrete mean square results .............................. 150
5.8 Proof of Theorem 5.16...................................... 153
6. Control systems and number theory 157
6.1 Introduction and preliminaries............................. 158
6.2 State space representation and the
visualization principle.................................... 158
6.3 Chain scattering representation............................ 163
6.4 Siegel upper space......................................... 165
Contents xiii
6.5 Norm of the function spaces................................. 167
6.6 (Unity) feedback system..................................... 170
6.7 J-lossless factorization and dualization.................... 171
6.8 FOPID controllers........................................... 173
6.9 Fourier, Mellin and (two-sided) Laplace
transforms................................................ 175
6.10 Examples of second-order systems and
their solution.............................................. 176
6.11 The product of zeta-functions: FF-type...................... 179
6.11.1 Statement of the situation.......................... 179
6.11.2 The Riesz sum: - .................... 182
Bibliography 187
Index 193
|
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| author | Li, Fuhuo Wang, Nianliang Kanemitsu, Shigeru |
| author_GND | (DE-588)104434251X (DE-588)1044342536 |
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| author_sort | Li, Fuhuo |
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| bvnumber | BV041965470 |
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| isbn | 9789814425636 |
| language | English |
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| physical | XIII, 194 S. |
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| publisher | World Scientific |
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| spelling | Li, Fuhuo Verfasser (DE-588)104434251X aut Number theory and its applications Fuhuo Li ; Nianliang Wang ; Shigeru Kanemitsu Singapore [u.a.] World Scientific 2013 XIII, 194 S. txt rdacontent n rdamedia nc rdacarrier Zahlentheorie (DE-588)4067277-3 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Wang, Nianliang Verfasser (DE-588)1044342536 aut Kanemitsu, Shigeru Verfasser aut http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=4944140&custom_att_2=simple_viewer Number theory and its applications Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027408227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Li, Fuhuo Wang, Nianliang Kanemitsu, Shigeru Number theory and its applications Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)1071861417 |
| title | Number theory and its applications |
| title_auth | Number theory and its applications |
| title_exact_search | Number theory and its applications |
| title_full | Number theory and its applications Fuhuo Li ; Nianliang Wang ; Shigeru Kanemitsu |
| title_fullStr | Number theory and its applications Fuhuo Li ; Nianliang Wang ; Shigeru Kanemitsu |
| title_full_unstemmed | Number theory and its applications Fuhuo Li ; Nianliang Wang ; Shigeru Kanemitsu |
| title_short | Number theory and its applications |
| title_sort | number theory and its applications |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie Konferenzschrift |
| url | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=4944140&custom_att_2=simple_viewer http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027408227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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