Diophantine Equations and Inequalities in Algebraic Number Fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1991
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s( k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert [1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here |
| Beschreibung: | 1 Online-Ressource (XVI, 170 p) |
| ISBN: | 9783642581717 9783642634895 |
| DOI: | 10.1007/978-3-642-58171-7 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Yuan, Wang |
| author_facet | Yuan, Wang |
| author_role | aut |
| author_sort | Yuan, Wang |
| author_variant | w y wy |
| building | Verbundindex |
| bvnumber | BV042422715 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-58171-7 |
| format | Electronic eBook |
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| id | DE-604.BV042422715 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642581717 9783642634895 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858132 |
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| publishDate | 1991 |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Yuan, Wang Verfasser aut Diophantine Equations and Inequalities in Algebraic Number Fields by Wang Yuan Berlin, Heidelberg Springer Berlin Heidelberg 1991 1 Online-Ressource (XVI, 170 p) txt rdacontent c rdamedia cr rdacarrier The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s( k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert [1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here Mathematics Number theory Number Theory Mathematik Diophantische Ungleichung (DE-588)4200628-4 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Kreismethode (DE-588)4260441-2 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Waringsches Problem (DE-588)4260442-4 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 s Diophantische Ungleichung (DE-588)4200628-4 s 1\p DE-604 Waringsches Problem (DE-588)4260442-4 s Kreismethode (DE-588)4260441-2 s 2\p DE-604 Diophantische Gleichung (DE-588)4012386-8 s 3\p DE-604 https://doi.org/10.1007/978-3-642-58171-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yuan, Wang Diophantine Equations and Inequalities in Algebraic Number Fields Mathematics Number theory Number Theory Mathematik Diophantische Ungleichung (DE-588)4200628-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd Kreismethode (DE-588)4260441-2 gnd Diophantische Gleichung (DE-588)4012386-8 gnd Waringsches Problem (DE-588)4260442-4 gnd |
| subject_GND | (DE-588)4200628-4 (DE-588)4068537-8 (DE-588)4260441-2 (DE-588)4012386-8 (DE-588)4260442-4 |
| title | Diophantine Equations and Inequalities in Algebraic Number Fields |
| title_auth | Diophantine Equations and Inequalities in Algebraic Number Fields |
| title_exact_search | Diophantine Equations and Inequalities in Algebraic Number Fields |
| title_full | Diophantine Equations and Inequalities in Algebraic Number Fields by Wang Yuan |
| title_fullStr | Diophantine Equations and Inequalities in Algebraic Number Fields by Wang Yuan |
| title_full_unstemmed | Diophantine Equations and Inequalities in Algebraic Number Fields by Wang Yuan |
| title_short | Diophantine Equations and Inequalities in Algebraic Number Fields |
| title_sort | diophantine equations and inequalities in algebraic number fields |
| topic | Mathematics Number theory Number Theory Mathematik Diophantische Ungleichung (DE-588)4200628-4 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd Kreismethode (DE-588)4260441-2 gnd Diophantische Gleichung (DE-588)4012386-8 gnd Waringsches Problem (DE-588)4260442-4 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Diophantische Ungleichung Algebraischer Zahlkörper Kreismethode Diophantische Gleichung Waringsches Problem |
| url | https://doi.org/10.1007/978-3-642-58171-7 |
| work_keys_str_mv | AT yuanwang diophantineequationsandinequalitiesinalgebraicnumberfields |