八上生物知识点总结
A Markov model for Selmer ranks in families of
太阳图案
twists
孕妇指南期刊名称： Compositio Mathematica
作者： Klagsbrun, Zev, Mazur, Barry, Rubin, Karl
丰满性感美女
年份： 2014年
跑步头晕
期号： 第07期
平安理赔系统关键词： elliptic curves; quadratic twists; Selmer groups; Markov process;猪肚炖什么养胃健脾
arithmetic statistics
摘要：We study the distribution of 2-Selmer ranks in the family of quadratic twists of an elliptic curve E over an arbitrary number field K. Under the assumption that Gal(K(E[2])/K) congruent to S-3, we show that the density (counted in a nonstandard way) of twists with Selmer rank r exists for all positive intege
rs r, and is given via an equilibrium distribution, depending only on a single parameter (the
'disparity'), of a certain Markov process that is itlf independent of E and K. More generally, our results also apply to p-Selmer ranks of twists of two-dimensional lf-dual F-p-reprentations of the absolute Galois group of K by characters of order p.生活中的启示
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