منابع مشابه
On the integrality of nth roots of generating functions
Motivated by the discovery that the eighth root of the theta series of the E8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ R (where R = 1 + xZ x ) can be written as f = gn for g ∈ R, n 2. Let Pn := {gn | g ∈R} and let μn := n∏p |n p. We show among other things that (i) for f ∈R, f ...
متن کاملPolynomials that Vanish on Distinct nth Roots of Unity
Let C denote the ̄eld of complex numbers and n the set of nth roots of unity. For t = 0; : : : ; n ¡ 1, de ̄ne the ideal =(n; t +1) 1⁄2 C [x0; : : : ; xt] consisting of those polynomials in t + 1 variables that vanish on distinct nth roots of unity; that is, f 2=(n; t+ 1) if and only if f (!0 ; : : : ; !t) = 0 for all (!0 ; : : : ; !t) 2 t+1 n satisfying !i 6= !j, for 0 · i < j · t. In this paper...
متن کاملA Parallel algorithm for principal nth roots of matrices
An iterative algorithm for computing the principal nth root of a positive deenite matrix is presented. The algorithm is based on the Gauss-Legendre approximation of a deenite integral. We p resent a parallelization in which we use as many processors as the order of the approximation. An analysis of the error introduced at each step of the iteration indicates that the algorithm converges more ra...
متن کاملnth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 2
Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.
متن کاملOn orbits of antichains of positive roots
For any finite poset P, there is a natural operator, X = XP, acting on the set of antichains of P. We discuss conjectural properties of X for some graded posets associated with irreducible root systems. In particular, if ∆ is the set of positive roots and Π is the set of simple roots in ∆, then we consider the cases P = ∆ and P = ∆ \ Π. For the root system of type An, we consider an X-invariant...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 1980
ISSN: 0002-9890
DOI: 10.2307/2321211