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The number of irreducible factors of a polynomial
 809–834; II, Acta Arith. 78 (1996), 125–142; III, Number theory in progress
, 1993
"... Abstract. Let F(x) be a polynomial with coefficients in an algebraic number field k. We estimate the number of irreducible cyclotomic factors of F in k[x], the number of irreducible noncyclotomic factors of F, the number of nth roots of unity among the roots of F, and the number of primitive nth roo ..."
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Cited by 12 (1 self)
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Abstract. Let F(x) be a polynomial with coefficients in an algebraic number field k. We estimate the number of irreducible cyclotomic factors of F in k[x], the number of irreducible noncyclotomic factors of F, the number of nth roots of unity among the roots of F, and the number of primitive nth
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 961 (11 self)
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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
The Parity of the Number of Irreducible Factors for Some Pentanomials
, 2008
"... It is well known that StickelbergerSwan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetran ..."
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Cited by 2 (1 self)
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It is well known that StickelbergerSwan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials
Parity of the Number of Irreducible Factors for Composite Polynomials
"... Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In thi ..."
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Cited by 1 (0 self)
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Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role
The Number Of Irreducible Factors Of A Polynomial, II
"... : Given a polynomial f 2 k[x], k a number field, we consider bounds on the number of cyclotomic factors of f appropriate when the number of nonzero coefficients of the polynomial, N(f ), is substantially less than than its degree. In particular we obtain bounds which (apart from a small degree depe ..."
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the number of irreducible factors of F in k[x] in terms of @(F ) and of the height H(F ) of the vector of coefficients of F . As is already clear from earlier work of Schinzel [6] and Dobrowolski [1], it is natural in problems of this type to give separate estimates for the number of cyclotomic factors
On the degrees of irreducible factors of higher order Bernoulli polynomials
 ACTA ARITHMETICA
, 1992
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ON IRREDUCIBLE FACTORS OF POLYNOMIALS OVER COMPLETE FIELDS
"... Abstract. Let (K, v) be a complete rank1 valued field. In this paper, we extend classical Hensel’s Lemma to residually transcendental prolongations of v to a simple transcendental extension K(x) and apply it to prove a generalization of Dedekind’s theorem regarding splitting of primes in algebraic ..."
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number fields. We also deduce an irreducibility criterion for polynomials over rank1 valued fields which extends already known generalizations of Schönemann Irreducibility Criterion for such fields. A refinement of Generalized Akira criterion proved in [Manuscripta Math., 134:12 (2010) 215224] is also
Irreducible factors of modular representations of mapping class groups arising in integral tqft
, 2012
"... Abstract. We find decomposition series of length at most two for modular representations in positive characteristic of mapping class groups of surfaces induced by an integral version of the WittenReshetikhinTuraev SO(3)TQFT at the pth root of unity, where p is an odd prime. The dimensions of the ..."
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of the irreducible factors are given by Verlindetype formulas. Contents
On The Degrees Of Irreducible Factors Of Polynomials Over A Finite Field
, 1999
"... Let F~_q[X] denote the multiplicative semigroup of monic polynomials in one indeterminate X over a finite field F_q. We determine for each fixed q... ..."
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Cited by 9 (0 self)
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Let F~_q[X] denote the multiplicative semigroup of monic polynomials in one indeterminate X over a finite field F_q. We determine for each fixed q...
Results 1  10
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788