As an application, we prove Herbrand's theorem which relates the nontriviality of certain parts of the ideal class group of (味 p ) to p dividing corresponding Bernoulli numbers. Then we calculate the index of the Stickelberger ideal in the group ring for (味 p n ) and find it equals...
赞同64 条评论 分享喜欢收藏申请转载 写下你的评论... 4 条评论 默认 最新 Lozen 作者 唔,这里有一些编号错误。这个错误来源于,我的pdf转图片软件只能转前5页,因此我其实是编译了两次的,结果就导致引用的编号实际上是正确的,但从第5页开始,命题等的编号错误 2020-05-04 ...
This paper explores the relation between the Eigenvalue Theorem and the work of Ludwig Stickelberger (1850–1936). To David Eisenbud on the occasion of his 75th birthday. Notes 1. If char(F) = p > 0, thenA = λIphas Tr(Aℓ) = 0 for allℓ ≥ 0, indepe...
In the next section, we construct explicit annihilators of An+ for every level n≥0 in the vein of the classical Stickelberger theorem. We begin with an explicit element that could be considered a “real” Gauss sum, and we explain how the factorization of this element gives rise to annih...
Kronecker-Weber via Stickelberger Franz Lemmermeyer Full-Text Cite this paper Add to My Lib Abstract: We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem. Full-Text Contact Us service@oalib.com QQ:3279437679 WhatsApp +8615387084133 ...
The theorem is this: Stickelberger"s Theorem . Let p be an odd prime, f a monk polynomial of degree d with coefficients in p [ x ], without repeated roots in any splitting field. Let r be the number of irreducible factors of f in p [ x ]. Then r≡d (mod 2) iff the ...
We develop the theory of Gauss sums to the extent needed for the proof of Stickelberger's theorem. In the final sections we provide deeper insight into the structure of Stickelberger's ideal. We determine its \\\(\\\mathbb{Z}\\\) -rank, find a free \\\(\\\mathbb{Z}\\\) -bas...
Stickelberger proved that the discriminant of a number field is congruent to 0 or 1 modulo 4. We generalize this to an arbitrary (not necessarily commutative) ring of finite rank over Z using techniques from linear algebra. Our proof relies on elementary matrix identities.Asher Auel...
The theorem of Stickelberger-Voronoi (cf. N. G. Chebotarev, Foundations of Galois Theory [in Russian], Vol. 2 (1937), p. 75) is extended to two unramified prime numbers in an algebraic number field. The proof is based on the following result: let K/k be a Galois extension of ...
Stickelberger's Theoremmulti-quadratic extensionsStark's ConjectureL-functionsannihilationclass-groupsWe prove, for all quadratic and a wide range of multi-quadratic extensions of global fields, a result concerning the annihilation as Galois modules of ideal class groups by explicit elements constructed ...