| 翻訳と辞書 |
| Oppenheim conjecture ： ウィキペディア英語版 |
Oppenheim conjecture
In Diophantine approximation, the Oppenheim conjecture concerns representations of numbers by real quadratic forms in several variables. It was formulated in 1929 by Alexander Oppenheim and later the conjectured property was further strengthened by Davenport and Oppenheim. Initial research on this problem took the number ''n'' of variables to be large, and applied a version of the Hardy-Littlewood circle method. The definitive work of Margulis, settling the conjecture in the affirmative, used methods arising from ergodic theory and the study of discrete subgroups of semisimple Lie groups.
== Short description ==
Meyer's theorem states that an indefinite integral quadratic form ''Q'' in ''n'' variables, ''n'' ≥ 5, nontrivially represents zero, i.e. there exists an non-zero vector ''x'' with integer components such that ''Q''(''x'') = 0. The Oppenheim conjecture can be viewed as an analogue of this statement for forms ''Q'' that are not multiples of a rational form. It states that in this case, the set of values of ''Q'' on integer vectors is a dense subset of the real line.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Oppenheim conjecture」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|