Results 21 to 30 of about 12,236 (229)
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
openaire +2 more sources
Mathematics, 2021 In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us to cover most known cases to date and provides a method which is amenable to generalizations to ...
Santiago Molina
doaj +1 more source
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)
openaire +2 more sources
Revisiting the Melvin-Morton-Rozansky expansion, or there and back again
Journal of High Energy Physics, 2020 Alexander polynomial arises in the leading term of a semi-classical Melvin-Morton-Rozansky expansion of colored knot polynomials. In this work, following the opposite direction, we propose how to reconstruct colored HOMFLY-PT polynomials ...
Sibasish Banerjee +2 more
doaj +1 more source
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
openaire +2 more sources
Properties of triple error orbits G and their invariants in Bose – Chaudhuri – Hocquenghem codes C7
Весці Нацыянальнай акадэміі навук Беларусі: Серыя фізіка-тэхнічных навук, 2019 This work is the further development of the theory of norms of syndromes: the theory of polynomial invariants of G-orbits of errors expands with the group G of automorphisms of binary cyclic BCH codes obtained by joining the degrees of cyclotomic ...
V. A. Lipnitski, A. U. Serada
doaj +1 more source
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
doaj +1 more source
Constacyclic Codes over Finite Chain Rings of Characteristic p
Axioms, 2021 Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R.
Sami Alabiad, Yousef Alkhamees
doaj +1 more source
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
core +4 more sources
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
openaire +2 more sources