Symmetric Non-Negative Forms and Sums of Squares
نویسندگان
چکیده
منابع مشابه
Sums of Squares of Linear Forms
Let k be a real field. We show that every non-negative homogeneous quadratic 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...
متن کاملBinary Forms as Sums of Two Squares and Châtelet Surfaces
— The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over Q.
متن کاملAutomorphic Forms and Sums of Squares over Function Fields
We develop some of the theory of automorphic forms in the function field setting. As an application, we find formulas for the number of ways a polynomial over a finite field can be written as a sum of k squares, k ≥ 2. Given a finite field Fq with q odd, we want to determine how many ways a polynomial in Fq[T ] can be written as a sum of k squares. For k ≥ 3 (or k = 2, −1 not a square in Fq), t...
متن کاملSubdiscriminant of symmetric matrices are sums of squares
In this Note we prove that the subdiscriminants of a symmetric matrix are sums of squares. This generalizes a result of [2] stating that the discriminant of a symmetric is a sum of squares and is inspired by its proof. A different, less explicit proof that the discriminant of a symmetric is a sum of squares also apear in [3]. As a consequence, we obtain an algebraic proof of the fact that all t...
متن کاملSums of squares of linear forms: the quaternions approach
Let A = k[y] be the polynomial ring in one single variable y over a field k. We discuss the number of squares needed to represent sums of squares of linear forms with coefficients in the ring A. We use quaternions to obtain bounds when the Pythagoras number of A is ≤ 4. This provides bounds for the Pythagoras number of algebraic curves and algebroid surfaces over k.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2020
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-020-00208-w