摘要
We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p > 3congruent to 3 modulo 4, the component e(p+1)/2of the p-Sylow subgroup of the ideal class group of Q(ζp) is trivial.
We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p 〉 3 congruent to 3 modulo 4, the component e（p＋1）/2 of the p-Sylow subgroup of the ideal class group of Q（ζp） is trivial.
基金
Supported by National Natural Science Foundation of China(Grant No.11171141)
Natural Science Foundation of Jiangsu Province of China(Grant Nos.BK2010007)
the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China(Grant No.708044)
