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The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
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 13 (2 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 982 (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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Cited by 1 (1 self)
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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
Bayes Factors
, 1995
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
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Cited by 1766 (74 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null
Results 1  10
of
108,998