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On the zeros of certain polynomials
 Proc. Amer. Math. Soc
"... Abstract. We prove that certain naturally arising polynomials have all of their roots on a vertical line. 1. The statement Given a rational function of the form P (t) = U(t), U(1) � = 0, (1 − t) d (1) where d ∈ N and U ∈ C[x] isofdegreee, there is a polynomial H ∈ C[x] ofdegree d − 1 such that if P ..."
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Cited by 20 (0 self)
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Abstract. We prove that certain naturally arising polynomials have all of their roots on a vertical line. 1. The statement Given a rational function of the form P (t) = U(t), U(1) � = 0, (1 − t) d (1) where d ∈ N and U ∈ C[x] isofdegreee, there is a polynomial H ∈ C[x] ofdegree d − 1
On derandomizing tests for certain polynomial identities
 In Proceedings of the Conference on Computational Complexity
, 2003
"... We extract a paradigm for derandomizing tests for polynomial identities from the recent AKS primality testing algorithm. We then discuss its possible application to other tests. 1 ..."
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Cited by 7 (2 self)
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We extract a paradigm for derandomizing tests for polynomial identities from the recent AKS primality testing algorithm. We then discuss its possible application to other tests. 1
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 962 (11 self)
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to be factored, n = deg(f) is the degree of f, and for a polynomial ~ a ~ i with real coefficients a i. i An outline of the algorithm is as follows. First we find, for a suitable small prime number p, a padic irreducible factor h of f, to a certain precision. This is done with Berlekamp's algorithm
− 227 − Certain Polynomials Related to Chebyshev Polynomials
"... Bae and Kim displayed a sequence of 4th degree selfreciprocal polynomials whose maximal zeros are related in a very nice and far from obvious way. The auxiliary polynomials in their results that parametrize their coefficients are of significant independent interest. In this note we show that such a ..."
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Bae and Kim displayed a sequence of 4th degree selfreciprocal polynomials whose maximal zeros are related in a very nice and far from obvious way. The auxiliary polynomials in their results that parametrize their coefficients are of significant independent interest. In this note we show
Casimir Elements for Certain Polynomial Current Lie Algebras
"... We consider the polynomial current Lie algebra 9 [(t)Ix] corresponding to the general linear Lie algebra [(r,), and its factoralgebra ., by the ideal Ek>., [(r*) x'k We construct two families of algebraically independent generators of the center of the universal enveloping algebra U(.,) by ..."
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Cited by 9 (1 self)
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We consider the polynomial current Lie algebra 9 [(t)Ix] corresponding to the general linear Lie algebra [(r,), and its factoralgebra ., by the ideal Ek>., [(r*) x'k We construct two families of algebraically independent generators of the center of the universal enveloping algebra U
An Algorithm to Calculate the Kernel of Certain Polynomial Ring Homomorphisms
 EXPERIMENTAL MATHEMATICS
, 1995
"... ..."
Uniqueness of certain polynomials constant on a hyperplane
, 2008
"... We study a question with connections to real algebraic geometry, combinatorics, and complex analysis. Let p(x,y) be a polynomial of degree d with N positive coefficients and no negative coefficients, such that p = 1 when x+y = 1. It is known that the sharp estimate d ≤ 2N −3 holds. In this paper we ..."
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We study a question with connections to real algebraic geometry, combinatorics, and complex analysis. Let p(x,y) be a polynomial of degree d with N positive coefficients and no negative coefficients, such that p = 1 when x+y = 1. It is known that the sharp estimate d ≤ 2N −3 holds. In this paper we
Uniqueness of certain polynomials constant on a hyperplane
, 2008
"... We study a question with connections to real algebraic geometry, combinatorics, and complex analysis. Let p(x,y) be a polynomial of degree d with N positive coefficients and no negative coefficients, such that p = 1 when x+y = 1. It is known that the sharp estimate d ≤ 2N −3 holds. In this paper we ..."
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We study a question with connections to real algebraic geometry, combinatorics, and complex analysis. Let p(x,y) be a polynomial of degree d with N positive coefficients and no negative coefficients, such that p = 1 when x+y = 1. It is known that the sharp estimate d ≤ 2N −3 holds. In this paper we
Results 1  10
of
295,301