Additive number theory of Polynomials over a finite field:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford
Clarendon Press
1991
|
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagwörter: | |
| Links: | 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 |
| Umfang: | XVI, 157 S. |
| ISBN: | 019853583X |
Internformat
MARC
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| 264 | 1 | |a Oxford |b Clarendon Press |c 1991 | |
| 300 | |a XVI, 157 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Oxford mathematical monographs | |
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| 650 | 4 | |a Nombres, Théorie des | |
| 650 | 7 | |a Nombres, théorie des |2 ram | |
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| 650 | 7 | |a corps fini |2 inriac | |
| 650 | 7 | |a fonction Dirichlet |2 inriac | |
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| 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 |
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| 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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| 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 |
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Datensatz im Suchindex
| _version_ | 1819248321810661376 |
|---|---|
| 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 |
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| 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 | 2024-12-20T08:33:19Z |
| 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 |
| 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 |
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