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Remarks on the Coefficients of Inverse Cyclotomic Polynomials
Mathematics, 2023 Cyclotomic polynomials play an imporant role in discrete mathematics. Recently, inverse cyclotomic polynomials have been defined and investigated.
Dorin Andrica, Ovidiu Bagdasar
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Combinatorial and harmonic-analytic methods for integer tilings
Forum of Mathematics, Pi, 2022 A finite set of integers A tiles the integers by translations if $\mathbb {Z}$ can be covered by pairwise disjoint translated copies of A. Restricting attention to one tiling period, we have $A\oplus B=\mathbb {Z}_M$ for some $M\in \mathbb {N}$ and $B ...
Izabella Łaba, Itay Londner
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Modified Cyclotomic Polynomial and Its Irreducibility
Mathematics, 2020 Finding irreducible polynomials over Q (or over Z ) is not always easy. However, it is well-known that the mth cyclotomic polynomials are irreducible over Q .
Ki-Suk Lee, Sung-Mo Yang, Soon-Mo Jung
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Defect and degree of the Alexander polynomial
European Physical Journal C: Particles and Fields, 2022 Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions of knot polynomials, i.e. of the non-perturbative Wilson averages in the Chern-Simons theory.
E. Lanina, A. Morozov
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Evolution properties of the knot’s defect
European Physical Journal C: Particles and Fields, 2022 The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is conjectured to be invariant under any antiparallel evolution and change linearly with the evolution in any parallel direction. In other words, each $${{\mathcal {R}}}$$
A. Morozov, N. Tselousov
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Efficient Algorithm for Finding Roots of Error-Locator Polynomials
IEEE Access, 2021 A novel method for finding roots of polynomials over finite fields has been proposed. This method is based on the cyclotomic discrete Fourier transform algorithm. The improvement is achieved by using the normalized cyclic convolutions, which have a small
Sergei Valentinovich Fedorenko
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Resultants of Cyclotomic Polynomials [PDF]
Proceedings of the American Mathematical Society, 1995 The authors calculate the resultant \(\text{Res}_x (\Phi_a (x^b), \Phi_c (x^d))\) for positive integers \(a,b,c,d\), where \(\Phi_n (x)\) is the \(n\)-th cyclotomic polynomial of degree \(\varphi (n)\). After establishing the factorization \(\Phi_a (x^b) = \prod_{[m,b] = ab} \Phi_m(x)\), they apply a chain rule for resultants to reduce the problem to ...
Cheng, Charles Ching-an +2 more
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Factoring with cyclotomic polynomials [PDF]
26th Annual Symposium on Foundations of Computer Science (sfcs 1985), 1985 This paper discusses some new integer factoring methods involving cyclotomic polynomials. There are several polynomials f ( X ) f(X) known to have the following property: given a multiple of f ( p ) f(p) , we can quickly split any composite number that has p ...
Bach, Eric, Shallit, Jeffrey
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High-Precision Leveled Homomorphic Encryption for Rational Numbers
Mathematics, 2023 In most homomorphic encryption schemes based on RLWE, native plaintexts are represented as polynomials in a ring Zt[x]/xN+1, where t is a plaintext modulus and xN+1 is a cyclotomic polynomial with a degree power of two.
Long Nie, Shaowen Yao, Jing Liu
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On Values of Cyclotomic Polynomials. V [PDF]
, 2003 In this paper, we present three results on cyclotomic polynomials. First, we present results about factorization of cyclotomic polynomials over arbitrary fields K.
Motose, Kaoru
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