Additive number theory of Polynomials over a finite field:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1991
|
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 157 S. |
| ISBN: | 019853583X |
Internformat
MARC
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| 100 | 1 | |a Effinger, Gove W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Additive number theory of Polynomials over a finite field |c Gove W. Effinger and David R. Hayes |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1991 | |
| 300 | |a XVI, 157 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford mathematical monographs | |
| 650 | 4 | |a Corps finis | |
| 650 | 7 | |a Corps finis |2 ram | |
| 650 | 4 | |a Nombres, Théorie des | |
| 650 | 7 | |a Nombres, théorie des |2 ram | |
| 650 | 4 | |a Polynômes | |
| 650 | 7 | |a Polynômes |2 ram | |
| 650 | 7 | |a corps fini |2 inriac | |
| 650 | 7 | |a fonction Dirichlet |2 inriac | |
| 650 | 7 | |a groupe Adele |2 inriac | |
| 650 | 7 | |a polynôme |2 inriac | |
| 650 | 7 | |a problème 3 nombres premiers |2 inriac | |
| 650 | 7 | |a problème Waring |2 inriac | |
| 650 | 7 | |a somme Gauss |2 inriac | |
| 650 | 7 | |a série singulière |2 inriac | |
| 650 | 7 | |a théorie additive |2 inriac | |
| 650 | 7 | |a théorie nombre |2 inriac | |
| 650 | 4 | |a Finite fields (Algebra) | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Polynomials | |
| 650 | 0 | 7 | |a Polynom |0 (DE-588)4046711-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Galois-Feld |0 (DE-588)4155896-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Additive Zahlentheorie |0 (DE-588)4141387-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
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| 689 | 1 | 0 | |a Additive Zahlentheorie |0 (DE-588)4141387-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Hayes, David R. |e Verfasser |4 aut | |
| 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=003394251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003394251 | ||
Datensatz im Suchindex
| _version_ | 1804119636252295168 |
|---|---|
| adam_text | Contents
List of symbols xiii
1 The polynomial Waring and Goldbach problems 1
1.1 The polynomial Waring problem 2
1.2 Sums of squares 7
1.3 The polynomial Goldbach problem 12
1.4 The circle method 13
1.5 The singular series 15
2 Local singular series 21
2.1 Fundamentals 21
2.2 Characters 23
2.3 Haar measure 25
2.4 Local Radon Nikodym derivatives 29
2.5 The case when S(h, V) is empty 32
3 Local Gauss sums and local derivatives 37
3.1 A Gauss sum on k,: definition and properties 37
3.2 A modified Gauss sum 40
ix
x Contents
3.3 Computation of some special local derivatives 43
3.4 The local derivative for Waring s problem 50
4 The adele ring over k 55
4.1 Definition and first properties 55
4.2 Adelic harmonic analysis 57
4.3 The character E 59
4.4 Global Radon Nikodym derivatives 62
4.5 The idele group of k 71
5 L functions of Dirichlet type 75
5.1 Multiplicative characters and L functions 75
5.2 The Riemann hypothesis 79
5.3 A brief historical note 83
5.4 A lower bound for the 3 primes singular series 84
6 The polynomial 3 primes generating function 89
6.1 Global Gauss sums and the summation Fr(t) 90
6.2 An estimate for £x€#|G(x,t)Mx 93
6.3 An asymptotic expression for Fr(t) and the fundamental do¬
mains 98
7 The polynomial 3 primes problem: an asymptotic
solution 103
7.1 Preliminary results 103
7.2 An asymptotic formula for N(M) 108
Contents xi
7.3 The 3 primes asymptotic theorem 120
8 The polynomial Waring problem 123
8.1 Major arc analysis 124
8.2 Minor arc analysis: Weyl s inequality for polynomials 130
8.3 The Waring singular series and the polynomial Waring theo¬
rem 137
Appendix A. A complete solution to the 3 primes
problem 141
Bibliography 145
Index 155
|
| any_adam_object | 1 |
| author | Effinger, Gove W. Hayes, David R. |
| author_facet | Effinger, Gove W. Hayes, David R. |
| author_role | aut aut |
| author_sort | Effinger, Gove W. |
| author_variant | g w e gw gwe d r h dr drh |
| building | Verbundindex |
| bvnumber | BV005429025 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA247.3 |
| callnumber-search | QA247.3 |
| callnumber-sort | QA 3247.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)24173362 (DE-599)BVBBV005429025 |
| dewey-full | 512.9/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/42 |
| dewey-search | 512.9/42 |
| dewey-sort | 3512.9 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005429025 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:29:20Z |
| institution | BVB |
| isbn | 019853583X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003394251 |
| oclc_num | 24173362 |
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| physical | XVI, 157 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Effinger, Gove W. Verfasser aut Additive number theory of Polynomials over a finite field Gove W. Effinger and David R. Hayes Oxford Clarendon Press 1991 XVI, 157 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Corps finis Corps finis ram Nombres, Théorie des Nombres, théorie des ram Polynômes Polynômes ram corps fini inriac fonction Dirichlet inriac groupe Adele inriac polynôme inriac problème 3 nombres premiers inriac problème Waring inriac somme Gauss inriac série singulière inriac théorie additive inriac théorie nombre inriac Finite fields (Algebra) Number theory Polynomials Polynom (DE-588)4046711-9 gnd rswk-swf Galois-Feld (DE-588)4155896-0 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Additive Zahlentheorie (DE-588)4141387-8 gnd rswk-swf Polynom (DE-588)4046711-9 s Galois-Feld (DE-588)4155896-0 s Zahlentheorie (DE-588)4067277-3 s DE-604 Additive Zahlentheorie (DE-588)4141387-8 s Hayes, David R. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003394251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Effinger, Gove W. Hayes, David R. Additive number theory of Polynomials over a finite field Corps finis Corps finis ram Nombres, Théorie des Nombres, théorie des ram Polynômes Polynômes ram corps fini inriac fonction Dirichlet inriac groupe Adele inriac polynôme inriac problème 3 nombres premiers inriac problème Waring inriac somme Gauss inriac série singulière inriac théorie additive inriac théorie nombre inriac Finite fields (Algebra) Number theory Polynomials Polynom (DE-588)4046711-9 gnd Galois-Feld (DE-588)4155896-0 gnd Zahlentheorie (DE-588)4067277-3 gnd Additive Zahlentheorie (DE-588)4141387-8 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4155896-0 (DE-588)4067277-3 (DE-588)4141387-8 |
| title | Additive number theory of Polynomials over a finite field |
| title_auth | Additive number theory of Polynomials over a finite field |
| title_exact_search | Additive number theory of Polynomials over a finite field |
| title_full | Additive number theory of Polynomials over a finite field Gove W. Effinger and David R. Hayes |
| title_fullStr | Additive number theory of Polynomials over a finite field Gove W. Effinger and David R. Hayes |
| title_full_unstemmed | Additive number theory of Polynomials over a finite field Gove W. Effinger and David R. Hayes |
| title_short | Additive number theory of Polynomials over a finite field |
| title_sort | additive number theory of polynomials over a finite field |
| topic | Corps finis Corps finis ram Nombres, Théorie des Nombres, théorie des ram Polynômes Polynômes ram corps fini inriac fonction Dirichlet inriac groupe Adele inriac polynôme inriac problème 3 nombres premiers inriac problème Waring inriac somme Gauss inriac série singulière inriac théorie additive inriac théorie nombre inriac Finite fields (Algebra) Number theory Polynomials Polynom (DE-588)4046711-9 gnd Galois-Feld (DE-588)4155896-0 gnd Zahlentheorie (DE-588)4067277-3 gnd Additive Zahlentheorie (DE-588)4141387-8 gnd |
| topic_facet | Corps finis Nombres, Théorie des Nombres, théorie des Polynômes corps fini fonction Dirichlet groupe Adele polynôme problème 3 nombres premiers problème Waring somme Gauss série singulière théorie additive théorie nombre Finite fields (Algebra) Number theory Polynomials Polynom Galois-Feld Zahlentheorie Additive Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003394251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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