The Hooley-Huxley contour method for problems in number fields II: factorization and divisibility
The Hooley-Huxley contour method for problems in number fields II: factorization and divisibility
复制标题
数域问题的Hooley-Huxley轮廓法II：因式分解和整除
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
M. D. Coleman
中科院分区：
文献类型：
--
作者：
M. D. Coleman
设L是数域K的伽罗瓦扩张。设n=n K=deg K/ℚ，n L=deg L/ℚ，n L/K=deg L/K。设I=I L/K表示K的分式理想群，其素分解不包含在L中分支的素理想，P={(α)ΣI：αΣK*，α>；0}.在Hecke[9}之后，令(λ1，λ2，…，λn−1)是P上满足λi(α)=1(1≤i≤n−1)的无挠特征标的基，对K的整数环中的所有单位α>；0。将每个λi的扩张固定到i上的一个特征标上，然后定义了λi，(α)(1≤i≤n−1)对K的所有不在L中分支的理想α.因此，对于这样的理想，我们可以定义。然后，上面提到的K的小区域是0 L，其记号是，对于任何α∈ℝ，我们设置β。在这里，β是唯一真正的讽刺。
Let L be a Galois extension of the number field K . Set n = n K = deg K/ℚ , n L = deg L /ℚ and n L / K = deg L/K . Let I = I L/K denote the group of fractional ideals of K whose prime decomposition contains no prime ideals that ramify in L , and let P = {(α)Σ I : αΣ K *, α>0}. Following Hecke [9}, let (λ 1 , λ 2 , …, λ n − 1 ) be a basis for the torsion-free characters on P that satisfy λ i (α) = 1 (1≤ i ≤ n − 1) for all units α>0 in , the ring of integers of K . Fixing an extension of each λ i to a character on I , then λ i ,( α ) (1 ≤ i ≤ n − 1) are defined for all ideals α of K that do not ramify in L . So, for such ideals, we can define . Then the small region of K referred to above is for 0 l with the notation that, for any α ∈ ℝ, we set β. where β is the unique real satisyfing .