Results 81 to 90 of about 12,236 (229)
Journal of Mathematical Cryptology, 2019 A family of ring-based cryptosystems, including the multilinear maps of Garg, Gentry and Halevi [Candidate multilinear maps from ideal lattices, Advances in Cryptology—EUROCRYPT 2013, Lecture Notes in Comput. Sci.
Biasse Jean-François, Song Fang
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On profinite rigidity amongst free‐by‐cyclic groups I: The generic case
Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.Abstract We prove that amongst the class of free‐by‐cyclic groups, Gromov hyperbolicity is an invariant of the profinite completion. We show that whenever G$G$ is a free‐by‐cyclic group with first Betti number equal to one, and H$H$ is a free‐by‐cyclic group which is profinitely isomorphic to G$G$, the ranks of the fibres and the characteristic ...
Sam Hughes, Monika Kudlinska
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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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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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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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Some <i>q</i>-supercongruences modulo the square and cube of a cyclotomic polynomial. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2021 Guo VJW, Schlosser MJ.
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Closed formulas for the factorization of $X^n-1$, the $n$-th cyclotomic polynomial, $X^n-a$ and $f(X^n)$ over a finite field for arbitrary positive integers $n$ [PDF]
, 2023 Anna-Maurin Graner
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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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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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