Applied Mathematics and Computation, ISSN 0096-3003, 03/2012, Volume 218, Issue 13, pp. 7014 - 7022

The number λq=2cos(π/q),q∈N,q⩾3, appears in the study of Hecke groups which are Fuchsian groups, and in the study of regular polyhedra. There are many partial...

Cyclotomic polynomials | Chebychev polynomials | Hecke groups | Minimal polynomials | Dickson polynomials | Möbius inversion | Mobius inversion | MATHEMATICS, APPLIED

Cyclotomic polynomials | Chebychev polynomials | Hecke groups | Minimal polynomials | Dickson polynomials | Möbius inversion | Mobius inversion | MATHEMATICS, APPLIED

Journal Article

Discrete Mathematics, ISSN 0012-365X, 12/2019, Volume 342, Issue 12, p. 111603

Let Fq be the finite field with q elements, where q is a prime power and let n be a positive integer. In this paper, we explore the factorization of f(xn) over...

Cyclotomic polynomials | Finite fields | [formula omitted]-constacyclic codes | Irreducible polynomials | MATHEMATICS | lambda-constacyclic codes | CONSTACYCLIC CODES

Cyclotomic polynomials | Finite fields | [formula omitted]-constacyclic codes | Irreducible polynomials | MATHEMATICS | lambda-constacyclic codes | CONSTACYCLIC CODES

Journal Article

Communications of the Korean Mathematical Society, ISSN 1225-1763, 2017, Volume 32, Issue 1, pp. 1 - 6

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 11/2016, Volume 62, Issue 11, pp. 6638 - 6643

One central theme in quantum error-correction is to construct quantum codes that have a relatively large minimum distance. In this paper, we first present a...

Reed-Solomon codes | cyclotomic coset | Quantum computing | polynomial code | Quantum mechanics | Linear codes | Electronic mail | Quantum code | Indexes | Cyclotomic coset | CONSTRUCTION | COMPUTER SCIENCE, INFORMATION SYSTEMS | LINEAR CODES | ENGINEERING, ELECTRICAL & ELECTRONIC | Polynomials | Quantum theory | Research | Parameters | Error correction | Information theory

Reed-Solomon codes | cyclotomic coset | Quantum computing | polynomial code | Quantum mechanics | Linear codes | Electronic mail | Quantum code | Indexes | Cyclotomic coset | CONSTRUCTION | COMPUTER SCIENCE, INFORMATION SYSTEMS | LINEAR CODES | ENGINEERING, ELECTRICAL & ELECTRONIC | Polynomials | Quantum theory | Research | Parameters | Error correction | Information theory

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2018, Volume 184, Issue 3, pp. 215 - 230

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 10/2019, Volume 13, Issue 2, pp. 605 - 618

Integral formulae for the coefficients of cyclotomic and polygonal polynomials were recently obtained in [2] and [3]. In this paper, we de ne and study a...

MATHEMATICS | MATHEMATICS, APPLIED | integral formula | cyclotomic polynomials | integer sequences | COEFFICIENTS | extended polygonal-type polynomials | polynomial coefficients | multinomial polynomials

MATHEMATICS | MATHEMATICS, APPLIED | integral formula | cyclotomic polynomials | integer sequences | COEFFICIENTS | extended polygonal-type polynomials | polynomial coefficients | multinomial polynomials

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 03/2012, Volume 218, Issue 13, pp. 7014 - 7022

The number =2cos(π/q),q∈N,q≥3, appears in the study of Hecke groups which are Fuchsian groups, and in the study of regular polyhedra. There are many partial...

Cyclotomic polynomials | Chebychev polynomials | Hecke groups | Minimal polynomials | Dickson polynomials | Möbius inversion | Algebra | Polyhedra | Computation | Mathematical analysis | Inversions | Polyhedrons | Mathematical models

Cyclotomic polynomials | Chebychev polynomials | Hecke groups | Minimal polynomials | Dickson polynomials | Möbius inversion | Algebra | Polyhedra | Computation | Mathematical analysis | Inversions | Polyhedrons | Mathematical models

Journal Article

Finite Fields and Their Applications, ISSN 1071-5797, 01/2018, Volume 49, pp. 156 - 165

Carlitz rank and index are two important measures for the complexity of a permutation polynomial f(x) over the finite field Fq. In particular, for...

Finite fields | Discrete logarithm | Linearity | Invertibility | Character sums | Permutation polynomials | Index | Carlitz rank | Cryptography | Cyclotomic mappings | MATHEMATICS, APPLIED | FINITE-FIELDS | MATHEMATICS

Finite fields | Discrete logarithm | Linearity | Invertibility | Character sums | Permutation polynomials | Index | Carlitz rank | Cryptography | Cyclotomic mappings | MATHEMATICS, APPLIED | FINITE-FIELDS | MATHEMATICS

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 2/2019, Volume 48, Issue 2, pp. 445 - 458

The Fourier coefficients of powers of the Dedekind eta function can be studied simultaneously. The vanishing of the coefficients varies from super lacunary...

Cyclotomic polynomials | Secondary 11F30 | Functions of a Complex Variable | 11P84 | Field Theory and Polynomials | Mathematics | Fourier coefficients | 11F20 | Dedekind eta function | Primary 11D10 | 11R18 | Fourier Analysis | 11B83 | Integer-valued polynomials | Number Theory | Combinatorics | MATHEMATICS

Cyclotomic polynomials | Secondary 11F30 | Functions of a Complex Variable | 11P84 | Field Theory and Polynomials | Mathematics | Fourier coefficients | 11F20 | Dedekind eta function | Primary 11D10 | 11R18 | Fourier Analysis | 11B83 | Integer-valued polynomials | Number Theory | Combinatorics | MATHEMATICS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 11/2017, Volume 13, Issue 10, pp. 2515 - 2530

We present a method to deal with the values of polynomials of type P ( z ) = ∏ d ∈ D ( 1 − z d ) j d on the unit circle. We use it to improve the known bounds...

relatives of cyclotomic polynomials | binary cyclotomic polynomial | jump one property | Cyclotomic polynomial | Beiter conjecture | ternary cyclotomic polynomial | unit circle | MATHEMATICS | COEFFICIENTS | JUMPS

relatives of cyclotomic polynomials | binary cyclotomic polynomial | jump one property | Cyclotomic polynomial | Beiter conjecture | ternary cyclotomic polynomial | unit circle | MATHEMATICS | COEFFICIENTS | JUMPS

Journal Article

Finite Fields and Their Applications, ISSN 1071-5797, 07/2013, Volume 22, pp. 57 - 69

We use cyclotomy to construct new classes of permutation polynomials over finite fields. This allows us to generate permutation polynomials in an algorithmic...

Finite fields | Permutation polynomials | Cyclotomy | Polynomials | Cyclotomic mappings | MATHEMATICS | ELEMENTS | MATHEMATICS, APPLIED | FINITE-FIELD PERMUTE

Finite fields | Permutation polynomials | Cyclotomy | Polynomials | Cyclotomic mappings | MATHEMATICS | ELEMENTS | MATHEMATICS, APPLIED | FINITE-FIELD PERMUTE

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2013, Volume 133, Issue 7, pp. 2455 - 2463

We revisit Stephen P. Humphriesʼ results indicating some connections between Chebyshev polynomials and twin primes, by using Chebyshev polynomials of the third...

Cyclotomic polynomial | Chebyshev polynomial | Twin prime | MATHEMATICS | INTERSECTION-NUMBER OPERATORS

Cyclotomic polynomial | Chebyshev polynomial | Twin prime | MATHEMATICS | INTERSECTION-NUMBER OPERATORS

Journal Article

Advances in Applied Mathematics, ISSN 0196-8858, 09/2018, Volume 100, pp. 43 - 70

Using some basic properties of the gamma function, we evaluate a simple class of infinite products involving Dirichlet characters as a finite product of gamma...

Cyclotomic polynomial | Infinite product | Gamma function | Multiple L-series | MATHEMATICS, APPLIED | Functional Analysis | Mathematics

Cyclotomic polynomial | Infinite product | Gamma function | Multiple L-series | MATHEMATICS, APPLIED | Functional Analysis | Mathematics

Journal Article

Journal of Number Theory, ISSN 0022-314X, 11/2016, Volume 168, pp. 154 - 166

In this paper, we give q-analogies of classical Kummer, Lucas and ASH (Anton, Stickelberger, Hensel)'s results on binomial coefficients modulo primes. Our...

Cyclotomic polynomials | Congruence | Binomial coefficients | Gaussian binomial coefficients | q-Series | Q-Series | MATHEMATICS | Q-ANALOGS

Cyclotomic polynomials | Congruence | Binomial coefficients | Gaussian binomial coefficients | q-Series | Q-Series | MATHEMATICS | Q-ANALOGS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 2012, Volume 132, Issue 3, pp. 410 - 413

We derive a lower and an upper bound for the number of binary cyclotomic polynomials Φ m with at most m 1 / 2 + ε nonzero terms.

Binary cyclotomic polynomial | Nonzero terms | MATHEMATICS

Binary cyclotomic polynomial | Nonzero terms | MATHEMATICS

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 4/2017, Volume 83, Issue 1, pp. 197 - 217

Let q be a prime power and let $${\mathbb {F}}_q$$ F q be a finite field with q elements. This paper discusses the explicit factorizations of cyclotomic...

Cyclotomic polynomials | Information and Communication, Circuits | Data Encryption | Irreducible factorization | Mathematics | 11B37 | Finite fields | 11T06 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | 12Y05 | Coding and Information Theory | 94A60 | Combinatorics | Irreducible polynomials | MATHEMATICS, APPLIED | DICKSON POLYNOMIALS | COMPUTER SCIENCE, THEORY & METHODS

Cyclotomic polynomials | Information and Communication, Circuits | Data Encryption | Irreducible factorization | Mathematics | 11B37 | Finite fields | 11T06 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | 12Y05 | Coding and Information Theory | 94A60 | Combinatorics | Irreducible polynomials | MATHEMATICS, APPLIED | DICKSON POLYNOMIALS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2015, Volume 435, pp. 223 - 262

By the Chinese remainder theorem, the canonical mapΨn:R[X]/(Xn−1)→⊕d|nR[X]/Φd(X) is an isomorphism when R is a field whose characteristic does not divide n and...

Cyclotomic polynomials | Resultant | Smith normal form | Bit complexity for computing Smith vectors | Bit complexity for computing smith vectors | MATHEMATICS | RESULTANTS | Algorithms

Cyclotomic polynomials | Resultant | Smith normal form | Bit complexity for computing Smith vectors | Bit complexity for computing smith vectors | MATHEMATICS | RESULTANTS | Algorithms

Journal Article

Finite Fields and Their Applications, ISSN 1071-5797, 01/2016, Volume 37, pp. 28 - 35

Let n∈Z+, and Φn(x) be the nth classical cyclotomic polynomial. In [4, Theorem 1], D. Lehmer showed that the geometric mean of {Φs(1):s,n∈Z+,s≤n}→e≈2.71828, as...

Carlitz cyclotomic polynomials | Pillai function | Carlitz polynomials | MSC 11R60 | 11A99 | 11G09 | MATHEMATICS | MATHEMATICS, APPLIED | Filial function

Carlitz cyclotomic polynomials | Pillai function | Carlitz polynomials | MSC 11R60 | 11A99 | 11G09 | MATHEMATICS | MATHEMATICS, APPLIED | Filial function

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 04/2016, Volume 106, Issue 4, pp. 345 - 353

Let q be an odd power of a prime p and let be a supersingular abelian variety of dimension g. We show that if , then the characteristic polynomial of the...

Cyclotomic polynomials | Weil polynomials | Supersingular | Abelian varieties | MATHEMATICS | ELLIPTIC-CURVES | FIELDS | SYSTEMS | IWASAWA THEORY | PRIMES | Mathematics - Number Theory

Cyclotomic polynomials | Weil polynomials | Supersingular | Abelian varieties | MATHEMATICS | ELLIPTIC-CURVES | FIELDS | SYSTEMS | IWASAWA THEORY | PRIMES | Mathematics - Number Theory

Journal Article

Journal of Number Theory, ISSN 0022-314X, 10/2014, Volume 143, pp. 102 - 108

We consider the analogue, when Z is replaced with Fq[T] of the elementary cyclotomic polynomials and prove an analogue of Suzuki's Theorem. For a video summary...

Carlitz cyclotomic polynomials | Carlitz polynomials | MATHEMATICS | COEFFICIENTS

Carlitz cyclotomic polynomials | Carlitz polynomials | MATHEMATICS | COEFFICIENTS

Journal Article

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