Vandiver猜想与非正则素数分布的一个猜想

The Vandiver Conjecture and a New Conjecture on the Distribution of Irregular Primes

本文介绍Vandiver猜想与相关研究结果;我们证明A2=A4=…=A_(32)=0,这里A是Q(ζp)的理想类群的p-Sylow子群;我们提出一个关于非正则素数分布的猜想,给出数值验算.

We give an introduction to the Vandiver conjecture and some related research in the literature.We show that Ao=A2=…=A_(32)=0,where A is the p-Sylow subgroup of the ideal class group of Q(Sp).Finally,we propose a new conjecture on the distribution of irregular primes with numerical verifications.