Results 21 to 30 of about 9,407 (175)
Vanishing sums of roots of unity and the Favard length of self-similar product sets
Discrete Analysis, 2022 Vanishing sums of roots of unity and the Favard length of self-similar product sets, Discrete Analysis 2022:19, 31 pp. An important theme in geometric measure theory is the typical size of a set when it is randomly projected. For example, suppose that $
Izabella Laba, Caleb Marshall
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CYCLOTOMIC POLYNOMIALS OVER CYCLOTOMIC FIELDS
Communications of the Korean Mathematical Society, 2012 In this paper, we find the minimal polynomial of a primitive root of unity over cyclotomic fields. From this, we factorize cyclotomic polynomials over cyclotomic fields and investigate the coefficients of when 3∤.
Sung-Doo Kim, June-Bok Lee
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Resultants of Cyclotomic Polynomials [PDF]
Proceedings of the American Mathematical Society, 1970 The author makes use of the lemma quoted in his previous review [Proc. Am. Math. Soc. 24, 482--485 (1970; Zbl 0188.34001)] to prove the following theorem concerning the resultant \(\rho(F_m,F_n)\) of two cyclotomic polynomials. If \(m>n>1\) and \((m,n)>1\), then \(\rho(F_m,F_n)=p^{\varphi(n)}\) if \(m/n\) is a power of a prime \(p\), and \(\rho(F_m,F_n)
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Calculating cyclotomic polynomials [PDF]
Mathematics of Computation, 2011 We present three algorithms to calculate Φ n ( z ) \Phi _n(z) , the n t h n_{th} cyclotomic polynomial. The first algorithm calculates Φ n ( z ) \Phi _n(z)
Arnold, Andrew, Monagan, Michael
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On Salem numbers, expansive polynomials and Stieltjes continued fractions [PDF]
, 2014 A converse method to the Construction of Salem (1945) of convergent families of Salem numbers is investigated in terms of an association between Salem polynomials and Hurwitz quotients via expansive polynomials of small Mahler measure.
Guichard, Christelle +1 more
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Cyclotomic expansion of generalized Jones polynomials [PDF]
Letters in Mathematical Physics, 2021 In previous work of the first and third authors, we proposed a conjecture that the Kauffman bracket skein module of any knot in $S^3$ carries a natural action of the rank 1 double affine Hecke algebra $SH_{q,t_1, t_2}$ depending on 3 parameters $q, t_1, t_2$.
Berest, Yuri +2 more
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On the k-error linear complexity of cyclotomic sequences [PDF]
, 2007 Exact values and bounds on the k-error linear complexity of p-periodic sequences which are constant on the cyclotomic classes are determined. This family of sequences includes sequences of discrete logarithms, Legendre sequences and Hall's sextic residue
Hassan, Aly +2 more
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Factorization of Graded Traces on Nichols Algebras
Axioms, 2017 A ubiquitous observation for finite-dimensional Nichols algebras is that as a graded algebra the Hilbert series factorizes into cyclotomic polynomials. For Nichols algebras of diagonal type (e.g., Borel parts of quantum groups), this is a consequence of ...
Simon Lentner, Andreas Lochmann
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Non-Beiter ternary cyclotomic polynomials with an optimally large set of coefficients
, 2011 Let l>=1 be an arbitrary odd integer and p,q and r primes.
Bachman G. +4 more
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Fractalized cyclotomic polynomials [PDF]
Proceedings of the American Mathematical Society, 2007 For each prime power p m p^m , we realize the classical cyclotomic polynomial Φ p m ( x ) \Phi _{p^m}(x) as one of a collection of 3 m 3^m different ...
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