例句與造句

1. Kolyvagin later used Heegner points to construct Euler systems, and used this to prove much of the Birch & ndash; Swinnerton-Dyer conjecture for rank 1 elliptic curves.
2. There was an error in one critical portion of the proof which gave a bound for the order of a particular group : the Euler system used to extend Flach's method was incomplete.
3. Karl Rubin found a more elementary proof of the Mazur-Wiles theorem by using Kolyvagin's Euler systems, described in and, and later proved other generalizations of the main conjecture for imaginary quadratic fields.
4. Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups.
5. Karl Rubin found a more elementary proof of the Mazur Wiles theorem by using Thaine's method and Kolyvagin's Euler systems, described in and, and later proved other generalizations of the main conjecture for imaginary quadratic fields.
6. It's difficult to find euler systems in a sentence. 用euler systems造句挺難的
7. In response, he approached colleagues to seek out any hints of cutting edge research and new techniques, and discovered an Euler system recently developed by Victor Kolyvagin and Matthias Flach that seemed " tailor made " for the inductive part of his proof.
8. Kazuya Kato refers to the elements in an Euler system as " arithmetic incarnations of zeta " and describes the property of being an Euler system as " an arithmetic reflection of the fact that these incarnations are related to special values of Euler products ".
9. Kazuya Kato refers to the elements in an Euler system as " arithmetic incarnations of zeta " and describes the property of being an Euler system as " an arithmetic reflection of the fact that these incarnations are related to special values of Euler products ".
10. For example, while Casti writes : " The problem with the proof lay in the construction of a complicated mathematical object called an Euler system, " the original text, according to the two societies, differs only in using the word " structure " rather than " object ."