Related papers: Gauss' lemma for polynomials over semidomains
We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouch\'{e} theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of…
We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Salem type and some linear recurrent sequences of Pisot type.…
In the present note a generalization of Borel-Cantelli Lemma is proposed.
In this paper, we investigated properties of Tribonacci-Lucas polynomials which generalized Tribonacci-Lucas numbers. From this generalization, we also obtain some new algebraic properties on these numbers and polynomials as Binet formula,…
We consider the ratio of two Gauss hypergeometric functions with real parameters shifted by arbitrary integers. We find a formula for the jump of this ratio over the branch cut in terms of a real hypergeometric polynomial, the beta density…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei…
Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras, with the single exception of Hamiltonian quaternions for…
Let K be a global field and f in K[X] be a polynomial. We present an efficient algorithm which factors f in polynomial time.
In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…
In this paper, as an analogue of the integer case, we study detailedly the period and the rank of the generalized Fibonacci sequence of polynomials over a finite field modulo an arbitrary polynomial. We establish some formulas to compute…
The classic Gauss-Lucas Theorem for complex polynomials of degree $d\ge2$ has a natural reformulation over quaternions, obtained via rotation around the real axis. We prove that such a reformulation is true only for $d=2$. We present a new…
The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction of an explicit basis of the space of…
Denote by $\Gamma$ the set of pointwise good sequences. Those are sequences of real numbers $(a_k)$ such that for any measure preserving flow $(U_t)_{t\in \mathbb R}$ on a probability space and for any $f\in L^\infty$, the averages…
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
We generalize Bulitko's Lemma to equations over (or homomorphisms into) groups that have $\kappa$-acylindrical splittings.
We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous known results concerning quasi-ordinary polynomials.
Generalized polynomials are mappings obtained from the conventional polynomials by the use of operations of addition, multiplication and taking the integer part. Extending the classical theorem of H. Weyl on equidistribution of polynomials,…
We prove some separation results for the roots of the generalized Fibonacci polynomials and their absolute values
In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds…