منابع مشابه
Galois Cohomology of Fields without Roots of Unity
There is a standard correspondence between elements of the cohomology group H(F, μn) (with the trivial action of ΓF = Gal(Fs/F ) on μn) and cyclic extensions of dimension n over F . We extend this to a correspondence between the cohomology groups H(F, μn) where the action of ΓF on μn varies, and the extensions of dimension n of K which are Galois over F , where K = F [μn] and [K :F ] is prime t...
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This text was originally intended for non-mathematicians; during its preparation B. Mazur and A. Wiles announced the solution of the ’Main Conjecture’ in the theory of cyclotomic fields. It seemed appropriate to us to try to give an explanation of what this sensational discovery is all about.
متن کاملRoots of unity in orders
We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in the group of roots of unity can be solved in polynomial time. As an auxiliary result, we solve the discrete logarithm problem for certain unit groups in finite...
متن کاملStable Computation of the Complex Roots of Unity Stable Computation of the Complex Roots of Unity
In this paper, we show that the problem of computing the complex roots of unity is not as simple as it seems at rst. In particular, the formulas given in a standard programmer's reference book Knuth, Seminumerical Algorithms, 1981] are shown to be numerically unstable, giving unacceptably large error for moderate sized sequences. We give alternative formulas, which we show to be superior both b...
متن کاملHall-Littlewood functions at roots of unity
Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using A. Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1988
ISSN: 0022-4049
DOI: 10.1016/0022-4049(88)90003-5