Results 71 to 80 of about 9,407 (175)
On Values of Cyclotomic Polynomials [PDF]
, 2001 The author proves that for an infinitely differentiable function \(g: \mathbb{R}_{>0} \to \mathbb{R}\) with \(g^{(k)} (x)> 0\) for all \(k\in \mathbb{N}_0\), \(x\in \mathbb{R}_{>0}\), and a natural number \(n\), the function \[ f_n (x)= \sum_{d\mid n} \mu(d) g\bigl( {\textstyle {n\over d}} x\bigr) \] is also arbitrarily often differentiable with \(f_n^{
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Cyclotomic polynomials and units in cyclotomic number fields
Journal of Number Theory, 1988 The author proves (theorem 1) that if P(x)\(\neq x\) is a monic irreducible polynomial with integer coefficients such that its resultant with infinitely many cyclotomic polynomials is \(+1\) or -1, then P(x) is a cyclotomic polynomial. From this he deduces a number of interesting corollaries: for example, if \(\alpha\neq 0\) is an algebraic integer ...
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A Note on Cyclotomic Polynomials
Rocky Mountain Journal of Mathematics, 1999 After recalling an identity concerning cyclotomic polynomials found by \textit{C. C. Cheng, J. H. McKay} and \textit{S. S. Wang} [Proc. Am. Math. Soc. 123, 1053-1059 (1995; Zbl 0828.11014)], the author gives three applications of it. First a description is given of polynomials \(f\in\mathbb{Z}[X]\) satisfying \(f(X)|f(X^n)\) for some fixed \(n\geq 2\).
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Functional tilings and the Coven-Meyerowitz tiling conditions
Discrete AnalysisFunctional tilings and the Coven-Meyerowitz tiling conditions, Discrete Analysis 2025:18, 20 pp. A finite set $A\subset\mathbb Z$ _tiles_ $\mathbb Z$ _by translations_ if $\mathbb Z$ can be covered by a union of disjoint translates of $A$.
Gergely Kiss +3 more
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Reciprocal cyclotomic polynomials
, 2007 Let $ _n(x)$ be the monic polynomial having precisely all non-primitive $n$th roots of unity as its simple zeros. One has $ _n(x)=(x^n-1)/ _n(x)$, with $ _n(x)$ the $n$th cyclotomic polynomial. The coefficients of $ _n(x)$ are integers that like the coefficients of $ _n(x)$ tend to be surprisingly small in absolute value, e.g.
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On computing factors of cyclotomic polynomials [PDF]
Mathematics of Computation, 1993 For odd square-free n > 1 n > 1 the cyclotomic polynomial Φ n ( x ) {\Phi _n}(x) satisfies the identity of Gauss, \[ 4 Φ n ( x
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Cyclotomic Completions of Polynomial Rings
Publications of the Research Institute for Mathematical Sciences, 2004 For a subset S ⊂ ℕ = \{1, 2, . . . \} and a commutative ring R with unit, let R[q]^S
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Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2023 Guo VJW, Schlosser MJ.
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New q-Analogues of Van Hamme's (E.2) Supercongruence and of a Supercongruence by Swisher. [PDF]
Results Math, 2023 Guo VJW, Schlosser MJ.
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The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings. [PDF]
Entropy (Basel), 2021 Ortiz JN +4 more
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