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 کاملsome properties of fuzzy hilbert spaces and norm of operators
in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1968-0225185-3