منابع مشابه
Solving algebraic equations in roots of unity
This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be described in terms of a finite number of parametric families called maximal torsion cosets. We obtain new explicit upper bounds for the number of maximal torsion cosets on an algebraic subvariety of the complex algebraic n-to...
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In a previous paper we demonstrated that Bethe’s equations are not sufficient to specify the eigenvectors of the XXZ model at roots of unity for states where the Hamiltonian has degenerate eigenvalues. We here find the equations which will complete the specification of the eigenvectors in these degenerate cases and present evidence that the sl2 loop algebra symmetry is sufficiently powerful to ...
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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...
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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 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...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1996
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-76-2-99-108