Factorization of irreducible polynomials over a finite field with the substitution for x
Andrew Long (1973)
Acta Arithmetica
Similarity:
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Andrew Long (1973)
Acta Arithmetica
Similarity:
Joshua Harrington, Lenny Jones (2013)
Colloquium Mathematicae
Similarity:
Let , where . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of on the coefficients of f(x) is the best possible in this situation.
John Garza (2014)
Acta Arithmetica
Similarity:
For an algebraic number field and a subset , we establish a lower bound for the average of the logarithmic heights that depends on the ideal of polynomials in vanishing at the point .
Stanislaw Lewanowicz (2002)
Applicationes Mathematicae
Similarity:
Let be any sequence of classical orthogonal polynomials. Further, let f be a function satisfying a linear differential equation with polynomial coefficients. We give an algorithm to construct, in a compact form, a recurrence relation satisfied by the coefficients in . A systematic use of the basic properties (including some nonstandard ones) of the polynomials results in obtaining a low order of the recurrence.
Stephan Ruscheweyh, Magdalena Wołoszkiewicz (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
Let be the uniform norm in the unit disk. We study the quantities where the infimum is taken over all polynomials of degree with and . In a recent paper by Fournier, Letac and Ruscheweyh (Math. Nachrichten 283 (2010), 193-199) it was shown that . We find the exact values of and determine corresponding extremal polynomials. The method applied uses known cases of maximal ranges of polynomials.
Joshua Harrington, Andrew Vincent, Daniel White (2013)
Journal de Théorie des Nombres de Bordeaux
Similarity:
In this paper we investigate the factorization of the polynomials in the special case where is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that is monic and linear.
Joe Callaghan (2007)
Annales Polonici Mathematici
Similarity:
Let K be any subset of . We define a pluricomplex Green’s function for θ-incomplete polynomials. We establish properties of analogous to those of the weighted pluricomplex Green’s function. When K is a regular compact subset of , we show that every continuous function that can be approximated uniformly on K by θ-incomplete polynomials, must vanish on . We prove a version of Siciak’s theorem and a comparison theorem for θ-incomplete polynomials. We compute when K is a compact...
Horst Alzer, Stamatis Koumandos (2006)
Colloquium Mathematicae
Similarity:
We prove: (I) For all integers n ≥ 2 and real numbers x ∈ (0,π) we have , with the best possible constant bounds α = (15-√2073)/10240 √(1998-10√2073) = -0.1171..., β = 1/3. (II) The inequality holds for all even integers n ≥ 2 and x ∈ (0,π), and also for all odd integers n ≥ 3 and x ∈ (0,π - π/n].
Zítko, Jan, Eliaš, Ján
Similarity:
The coefficients of the greatest common divisor of two polynomials and (GCD) can be obtained from the Sylvester subresultant matrix transformed to lower triangular form, where and deg(GCD) needs to be computed. Firstly, it is supposed that the coefficients of polynomials are given exactly. Transformations of for an arbitrary allowable are in details described and an algorithm for the calculation of the GCD is formulated. If inexact polynomials are given, then an approximate...
Daniel Carando, Damián Pinasco, Jorge Tomás Rodríguez (2013)
Studia Mathematica
Similarity:
For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on , whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also holds for the Schatten classes . For p > 2 we present some estimates on the constants involved.
Katarzyna Grasela (2010)
Banach Center Publications
Similarity:
We consider the space of ultradifferentiable functions with compact supports and the space of polynomials on . A description of the space of polynomial ultradistributions as a locally convex direct sum is given.
Maritza M. Branker (2005)
Annales Polonici Mathematici
Similarity:
We apply pluripotential theory to establish results in concerning uniform approximation by functions of the form wⁿPₙ where w denotes a continuous nonnegative function and Pₙ is a polynomial of degree at most n. Then we use our work to show that on the intersection of compact sections a continuous function on Σ is uniformly approximable by θ-incomplete polynomials (for a fixed θ, 0 < θ < 1) iff f vanishes on θ²Σ. The class of sets Σ expressible as the intersection of compact...
L. Carlitz, H. M. Srivastava (1976)
Matematički Vesnik
Similarity:
L. Carlitz, H. M. Srivastava (1976)
Matematički Vesnik
Similarity:
V. Flammang (2016)
Colloquium Mathematicae
Similarity:
Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates are positive real numbers. We study the set ₂ of the quantities . We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.
Wojciech Banaszczyk, Artur Lipnicki (2015)
Annales Polonici Mathematici
Similarity:
The paper deals with the approximation by polynomials with integer coefficients in , 1 ≤ p ≤ ∞. Let be the space of polynomials of degree ≤ n which are divisible by the polynomial , r ≥ 0, and let be the set of polynomials with integer coefficients. Let be the maximal distance of elements of from in . We give rather precise quantitative estimates of for n ≳ 6r. Then we obtain similar, somewhat less precise, estimates of for p ≠ 2. It follows that as n → ∞. The results...
Guillermo Matera, Mariana Pérez, Melina Privitelli (2014)
Acta Arithmetica
Similarity:
We obtain an estimate on the average cardinality (d,s,a) of the value set of any family of monic polynomials in of degree d for which s consecutive coefficients are fixed. Our estimate asserts that , where . We also prove that , where ₂(d,s,a) is the average second moment of the value set cardinalities for any family of monic polynomials of of degree d with s consecutive coefficients fixed as above. Finally, we show that , where ₂(d,0) denotes the average second moment for...
Jeffrey S. Geronimo, Plamen Iliev (2014)
Journal of the European Mathematical Society
Similarity:
We give a complete characterization of the positive trigonometric polynomials on the bi-circle, which can be factored as where is a polynomial nonzero for and . The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight on the bi-circle. We use this result to describe how specific factorizations of weights on the bi-circle can be translated into identities...
Didier D&#039;Acunto, Krzysztof Kurdyka (2005)
Annales Polonici Mathematici
Similarity:
Let f: ℝⁿ → ℝ be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Łojasiewicz’s gradient inequality states that there exist C > 0 and ϱ ∈ (0,1) such that in a neighbourhood of the origin. We prove that the smallest such exponent ϱ is not greater than with .