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On the rank of a binary form
"... Abstract. We describe in the space of binary forms of degree d the strata of forms having constant rank. We also give a simple algorithm to determine the rank of a given form. 1. ..."
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Abstract. We describe in the space of binary forms of degree d the strata of forms having constant rank. We also give a simple algorithm to determine the rank of a given form. 1.
Higher discriminants of binary forms ∗
, 2008
"... We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree. ..."
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We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree.
INVARIANTS OF POLYNOMIALS AND BINARY FORMS
"... Abstract. We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4. 1. ..."
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Abstract. We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4. 1.
Powerfree Values of Binary Forms
 Journal of Number Theory
, 1994
"... this paper, we will also consider f to be irreducible. We set n = deg f . For k = 2, this problem has recently become of interest partially because of its connection to the rank of elliptic curves as described in the work of F. Gouvea and B. Mazur [4]. In particular, F. Gouvea and B. Mazur showed th ..."
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Cited by 3 (1 self)
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that if the degree of the binary form is 3, then f(a; b) is squarefree for infinitely many pairs of integers a and b. More specifically, for a binary form f(x; y) 2 Z[x; y] of degree 3, they determined the density of pairs (a; b)
On the Wronskian combinants of binary forms
"... Abstract. For generic binary forms A1,...,Ar of order d we construct a class of combinants C = {Cq: 0 ≤ q ≤ r,q ̸ = 1}, to be called the Wronskian combinants of the Ai. We show that the collection C gives a projective imbedding of the Grassmannian G(r,Sd), and as a corollary, any other combinant adm ..."
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Cited by 5 (1 self)
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Abstract. For generic binary forms A1,...,Ar of order d we construct a class of combinants C = {Cq: 0 ≤ q ≤ r,q ̸ = 1}, to be called the Wronskian combinants of the Ai. We show that the collection C gives a projective imbedding of the Grassmannian G(r,Sd), and as a corollary, any other combinant
The length of binary forms
"... Abstract. The Klength of a form f in K[x1,..., xn], K ⊂ C, is the smallest number of dth powers of linear forms of which f is a Klinear combination. We present many results, old and new, about Klength, mainly in n = 2, and often about the length of the same form over different fields. For exampl ..."
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Cited by 5 (1 self)
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Abstract. The Klength of a form f in K[x1,..., xn], K ⊂ C, is the smallest number of dth powers of linear forms of which f is a Klinear combination. We present many results, old and new, about Klength, mainly in n = 2, and often about the length of the same form over different fields
On the typical rank of real binary forms
, 2009
"... We determine the rank of a general real binary form of degree d = 4 and d = 5. In the case d = 5, the possible values of the rank of such general forms are 3, 4, 5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d. ..."
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We determine the rank of a general real binary form of degree d = 4 and d = 5. In the case d = 5, the possible values of the rank of such general forms are 3, 4, 5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d.
Results 1  10
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734,562