某些實(shí)二次域狹義類群的8－秩.pdf

1、南京航空航天大學(xué)碩士學(xué)位論文某些實(shí)二次域狹義類群的8－秩姓名：張玲瑞申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：岳勤20061201某些實(shí)二次域狹義類群的 8－秩 iiAbstract It is one of important subjects in algebraic number theory to study the class number of a number field. In a decomposition of th

2、e 2-Sylow subgroup of the class group of a quadratic number field into cyclic subgroup summands, counting the number of summands of order at most 8, namely the 8-rank of class group, becomes significant. This paper mainl

3、y investigates the 8-ranks of real quadratic fields ( ) F d = ? , where , 1mod 4 d pq p q δ = ≡ ≡ and 1 2 3, d p p p δ = 1mod 4, 1,2,3 i p i ≡ = , {1,2} δ ∈ , are squarefree positive integers, gives the necessary an

4、d sufficient conditions of 8-ranks of their narrow class groups equal to 1 or 2, and determines whether the norms of their fundamental units are 1 or -1 in certain cases. This paper uses genus theory, Rédei matrix,

5、Gauss theorem, and Legendre theorem to get these results. They are in terms of congruence relations modulo prime, Legendre symbol and quartic residue symbol and so on. They are very useful for numerical computations. Ke