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...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.展开更多
Using the idea of Sinnott,Gillard and Schneps,we prove theμ-invariant is zero for the two-variable primitive p-adic L-function constructed by Kang(2012),which arises naturally in the study of Iwasawa theory for an el...Using the idea of Sinnott,Gillard and Schneps,we prove theμ-invariant is zero for the two-variable primitive p-adic L-function constructed by Kang(2012),which arises naturally in the study of Iwasawa theory for an elliptic curve with complex multiplication(CM).展开更多
Let F be a cubic cyclic field with t(2)ramified primes.For a finite abelian group G,let r3(G)be the 3-rank of G.If 3 does not ramify in F,then it is proved that t-1 r3(K2O F)2t.Furthermore,if t is fixed,for any s sati...Let F be a cubic cyclic field with t(2)ramified primes.For a finite abelian group G,let r3(G)be the 3-rank of G.If 3 does not ramify in F,then it is proved that t-1 r3(K2O F)2t.Furthermore,if t is fixed,for any s satisfying t-1 s 2t-1,there is always a cubic cyclic field F with exactly t ramified primes such that r3(K2O F)=s.It is also proved that the densities for 3-ranks of tame kernels of cyclic cubic number fields satisfy a Cohen-Lenstra type formula d∞,r=3-r2∞k=1(1-3-k)r k=1(1-3-k)2.This suggests that the Cohen-Lenstra conjecture for ideal class groups can be extended to the tame kernels of cyclic cubic number fields.展开更多
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)
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 11171141)the State Key Development Program for Basic Research of China (973 Program) (Grant No. 2013CB834202)+2 种基金Natural Science Foundation of Jiangsu Province of China (NSFJ) (Grant No. BK2010007)a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China (Grant No. 708044)
文摘Using the idea of Sinnott,Gillard and Schneps,we prove theμ-invariant is zero for the two-variable primitive p-adic L-function constructed by Kang(2012),which arises naturally in the study of Iwasawa theory for an elliptic curve with complex multiplication(CM).
基金supported by National Natural Science Foundation of China (Grant Nos. 11201225,11271177,10971091 and 11171141)Natural Science Foundation of the Jiangsu Province (Grant Nos. BK2010007 and BK2010362)Program for New Century Excellent Talents in University (Grant No. NCET-100471)
文摘Let F be a cubic cyclic field with t(2)ramified primes.For a finite abelian group G,let r3(G)be the 3-rank of G.If 3 does not ramify in F,then it is proved that t-1 r3(K2O F)2t.Furthermore,if t is fixed,for any s satisfying t-1 s 2t-1,there is always a cubic cyclic field F with exactly t ramified primes such that r3(K2O F)=s.It is also proved that the densities for 3-ranks of tame kernels of cyclic cubic number fields satisfy a Cohen-Lenstra type formula d∞,r=3-r2∞k=1(1-3-k)r k=1(1-3-k)2.This suggests that the Cohen-Lenstra conjecture for ideal class groups can be extended to the tame kernels of cyclic cubic number fields.
