IRREDUCIBILITY CRITERIA FOR SUMS OF TWO RELATIVELY PRIME POLYNOMIALS
نویسندگان
چکیده
منابع مشابه
When are Two Numerical Polynomials Relatively Prime?
Let a and b be two polynomials having numerical coeecients. We consider the question: when are a and b relatively prime? Since the coeecients of a and b are approximant, the question is the same as: when are two polynomials relatively prime, even after small perturbations of the coeecients? In this paper we provide a numeric parameter for determining that two polynomials are prime, even under s...
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In 1857 Bouniakowsky [6] made a conjecture concerning prime values of polynomials that would, for instance, imply that x + 1 is prime for infinitely many integers x. Let ƒ (x) be a polynomial with integer coefficients and define the fixed divisor of ƒ, written d(ƒ), as the largest integer d such that d divides f(x) for all integers x. Bouniakowsky conjectured that if f(x) is nonconstant and irr...
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The probability for two monic polynomials of a positive degree n with coefficients in the finite field Fq to be relatively prime turns out to be identical with the probability for an n × n Hankel matrix over Fq to be nonsingular. Motivated by this, we give an explicit map from pairs of coprime polynomials to nonsingular Hankel matrices that explains this connection. A basic tool used here is th...
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In this note, we show that if the characteristic polynomial of some Hecke operator Tn acting on the space of weight k cusp forms for the group SL2(Z ) is irreducible, then the same holds for Tp, where p runs through a density one set of primes. This proves that if Maeda’s conjecture is true for some Tn, then it is true for Tp for almost all primes p.
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2013
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042113500413