Add to ORKGAbstract. Let k be a real field. We show that every non-negative homogeneous qua-dratic polynomial f(x1,..., xn) with coefficients in the polynomial ring k[t] is a sum of 2n · τ(k) squares of linear forms, where τ(k) is the supremum of the levels of the finite non-real field extensions of k. From this result we deduce bounds for the Pythagoras numbers of affine curves over fields, and of excellent two-dimensional local henselian rings
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
AbstractWe prove first that, for fixed integers n, m⩾1, there is a uniform bound on the number of Pf...
This paper presents lower and upper bounds on the Pythagoras number of sum of square magnitudes of c...
Abstract. Let k be a real field. We show that every non-negative homogeneous qua-dratic polynomial f...
AbstractHilbert’s 17th Problem launched a number of inquiries into sum-of-squares representations of...
Let $n\in\mathbb{N}$ and let $K$ be a field with a henselian discrete valuation of rank $n$ with her...
AbstractIn this paper, we study the number of representations of polynomials of the ringFq[T] by dia...
We bound the Pythagoras number of a real projective subvariety: the smallest positive integer $r$ su...
We study sums of squares in algebraic function fields over formally real fields, in particular the a...
We study sums of squares in algebraic function fields over formally real fields, in particular the a...
We study sums of squares in algebraic function fields over formally real fields, in particular the a...
AbstractWe develop some of the theory of automorphic forms in the function field setting. As an appl...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 ...
AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 ...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
AbstractWe prove first that, for fixed integers n, m⩾1, there is a uniform bound on the number of Pf...
This paper presents lower and upper bounds on the Pythagoras number of sum of square magnitudes of c...
Abstract. Let k be a real field. We show that every non-negative homogeneous qua-dratic polynomial f...
AbstractHilbert’s 17th Problem launched a number of inquiries into sum-of-squares representations of...
Let $n\in\mathbb{N}$ and let $K$ be a field with a henselian discrete valuation of rank $n$ with her...
AbstractIn this paper, we study the number of representations of polynomials of the ringFq[T] by dia...
We bound the Pythagoras number of a real projective subvariety: the smallest positive integer $r$ su...
We study sums of squares in algebraic function fields over formally real fields, in particular the a...
We study sums of squares in algebraic function fields over formally real fields, in particular the a...
We study sums of squares in algebraic function fields over formally real fields, in particular the a...
AbstractWe develop some of the theory of automorphic forms in the function field setting. As an appl...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 ...
AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 ...
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of s...
AbstractWe prove first that, for fixed integers n, m⩾1, there is a uniform bound on the number of Pf...
This paper presents lower and upper bounds on the Pythagoras number of sum of square magnitudes of c...