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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2016, Volume 436, Issue 1, pp. 489 - 500
Let α be a totally positive algebraic integer, and define its absolute trace to be Tr(α)deg(α), the trace of α divided by the degree of α. Elementary... 
Totally positive algebraic number | Minimal polynomial | Schur–Siegel–Smyth trace problem | Schur-Siegel-Smyth trace problem | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE ALGEBRAIC-INTEGERS | VALUES
Journal Article
Journal of Number Theory, ISSN 0022-314X, 03/2016, Volume 160, pp. 409 - 417
In 1993 Estes and Guralnick conjectured that any totally real separable monic polynomial with rational integer coefficients will occur as the minimal... 
Minimal polynomials | Salem numbers | POLYNOMIALS | MATHEMATICS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2014, Volume 444, pp. 227 - 230
Let A be a connected integer symmetric matrix, i.e., A=(aij)∈Mn(Z) for some n, A=AT, and the underlying graph (vertices corresponding to rows, with vertex i... 
Trace problem | Minimal polynomials | Integer symmetric matrices | MATHEMATICS, APPLIED | ALGEBRAIC-INTEGERS | SALEM-NUMBERS
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 04/2009, Volume 78, Issue 266, pp. 1119 - 1125
Explicit auxiliary functions can be used in the ``Schur-Siegel- Smyth trace problem''. In the previous works, these functions were constructed only with... 
Integers | Local minimum | Numbers | Algebra | Mathematical tables | Polynomials | Mathematical functions | Mathematical inequalities | Complex roots | Degrees of polynomials | POLYNOMIALS | COEFFICIENTS | MATHEMATICS, APPLIED | NUMBERS
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2019, Volume 65, Issue 4, pp. 2101 - 2106
In this paper, we construct some class of explicit subcovers of the curve X n,r defined over F q(n) by affine equation y q(n-1) + ··· + y q + y = x q(n-r)+1 -... 
Codes | AG codes | subcover | Polynomials | Trace-defining curves | Topology | Mathematical model | Weierstrass semigroup | CASTLE | COMPUTER SCIENCE, INFORMATION SYSTEMS | MINIMUM DISTANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Formulas (mathematics)
Journal Article
Finite Fields and their Applications, ISSN 1071-5797, 11/2008, Volume 14, Issue 4, pp. 1002 - 1009
The extension field F where q is a prime divisor of (P - 1), has a unique structure. This paper describes this unique structure and uses it to derive formulas... 
Trace | Reciprocal polynomial | Root computation
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2006, Volume 75, Issue 253, pp. 385 - 393
For all totally positive algebraic numbers \alpha except a finite number of explicit exceptions, the following inequality holds: \[... 
Integers | Local minimum | Algebra | Heuristics | Mathematical tables | Polynomials | Mathematical functions | Mathematical inequalities | Coefficients | Algebraic conjugates | MATHEMATICS, APPLIED
Journal Article
Journal of Number Theory, ISSN 0022-314X, 02/2016, Volume 159, pp. 402 - 425
We establish a relation between minimal value set polynomials defined over Fq and certain q-Frobenius nonclassical curves. The connection leads to a... 
Frobenius nonclassical curve | Finite field | Minimal value set polynomial | POLYNOMIALS | TRACE | MATHEMATICS | GENERALIZED HERMITIAN CODES | FINITE-FIELDS | NORM | PLANE-CURVES
Journal Article
Asian-European Journal of Mathematics, ISSN 1793-5571, 03/2015, Volume 8, Issue 1
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2019, Volume 65, Issue 4, pp. 2593 - 2602
Journal Article
Acta Mathematica Vietnamica, ISSN 0251-4184, 3/2016, Volume 41, Issue 1, pp. 171 - 181
First, we study linear equations over finite fields in general. An explicit formula for a common period is found for every solution of a linear difference... 
Trace representation | Characteristic equations | Jordan multiplicative decomposition | Lucas’ congruence | 12Y05 | 12E20 | Mathematics, general | Mathematics | Max-sequences | Minimal polynomial
Journal Article
Experimental Mathematics, ISSN 1058-6458, 01/2014, Volume 23, Issue 1, pp. 1 - 5
In this paper, we give a list of monic integer polynomials of smallest possible trace, irreducible, of degree 16, and having all roots real and positive.... 
Schur-Siegel-Smyth Trace Problem | polynomials with minimal trace | auxiliary functions | Auxiliary functions | Polynomials with minimal trace | MATHEMATICS | 11C08 | 11R09 | 11S05 | 26C10 | 90C11 | 12D10 | ALGEBRAIC-INTEGERS | Continental interfaces, environment | Sciences of the Universe | Environmental Sciences
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2013, Volume 141, Issue 9, pp. 2963 - 2978
We provide a necessary and sufficient condition for a simple object in a pivotal \Bbbk minimal model in conformal field theory, and quantum groups at a root of... 
DIMENSIONAL HOPF-ALGEBRAS | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | LIE SUPER-ALGEBRAS | REPRESENTATIONS | INVARIANTS | DELIGNES CATEGORY | SUPERALGEBRAS | FORMULA | FINITE TENSOR CATEGORIES | CHARACTERS | Quantum Algebra | Mathematics | Representation Theory
Journal Article
2014 IEEE International Conference on Information and Automation (ICIA), 07/2014, pp. 137 - 140
The paper described a novel method of computing the trace of an element from a given finite field GF(p n ). By applying the Newton Formula, this method shows a... 
Finite Fields | Abstracts | Educational institutions | Minimal Polynomial | Polynomials | Finite element analysis | Cryptography | Galois fields | Trace Computation
Conference Proceeding
Finite Fields and Their Applications, ISSN 1071-5797, 2008, Volume 14, Issue 4, pp. 1002 - 1009
The extension field F P q where q is a prime divisor of ( P − 1 ) , has a unique structure. This paper describes this unique structure and uses it to derive... 
Trace | Reciprocal polynomial | Root computation
Journal Article
Taiwanese Journal of Mathematics, ISSN 1027-5487, 2/2008, Volume 12, Issue 1, pp. 245 - 253
We study polynomials over finite fields with a given value set. By constructing relations among the coefficients of Lagrange Interpolation Formula of these... 
Integers | Cardinality | Mathematical sets | Polynomials | Mathematics | Coefficients | Degrees of polynomials | Trace | Finite field | Minimal value set polynomial | Value set | MATHEMATICS | trace | minimal value set polynomial | finite field | value set
Journal Article
FINITE FIELDS AND THEIR APPLICATIONS, ISSN 1071-5797, 11/2008, Volume 14, Issue 4, pp. 1002 - 1009
The extension field F-Pq where q is a prime divisor of (P - 1), has a unique structure. This paper describes this unique structure and uses it to derive... 
Trace | MATHEMATICS | MATHEMATICS, APPLIED | Reciprocal polynomial | Root computation
Journal Article
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