𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Isotropy of Six-Dimensional Quadratic Forms over Function Fields of Quadrics

✍ Scribed by Oleg T Izhboldin; Nikita A Karpenko

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
347 KB
Volume
209
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let F be a field of characteristic different from 2 and let Ο† be an anisotropic six-dimensional quadratic form over F. We study the last open cases in the problem of describing the quadratic forms ψ such that Ο† becomes isotropic over the function field F ψ .

πŸ“œ SIMILAR VOLUMES

Pencils of Quadratic Forms and Hyperelli
Pencils of Quadratic Forms and Hyperelliptic Function Fields
✍ David B. Leep; Laura Mann Schueller πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 126 KB

Let P k denote the set of equivalence classes of nonsingular pencils of Ε½ . quadratic forms of even order defined over a field k, char k / 2. Let F k denote the set of k-isomorphism classes of hyperelliptic function fields defined over k. We Ε½ . Ε½ . define a map ⌽: P k Βͺ F k and determine precisely

Classification of Quadratic Forms over S
Classification of Quadratic Forms over Skew Fields of Characteristic 2
✍ Mohamed Abdou Elomary; Jean-Pierre Tignol πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 188 KB

Quadratic forms over division algebras over local or global fields of characteristic 2 are classified by an invariant derived from the Clifford algebra construction.

Automorphic Forms and Sums of Squares ov
Automorphic Forms and Sums of Squares over Function Fields
✍ Jeffrey Hoffstein; Kathy D. Merrill; Lynne H. Walling πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 206 KB

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. As a consequence, we show every polynomial can be written as a sum of 4 squares. We

Zeros of a Pair of Quadratic Forms Defin
Zeros of a Pair of Quadratic Forms Defined over a Finite Field
✍ David B. Leep; Laura Mann Schueller πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 155 KB

Let N be the number of affine zeros of a pair of quadratic forms in n#1 variables defined over a finite field F O . We give upper and lower bounds for N and show that these bounds are optimal. One result states that if n#1510 and every quadratic form in the pencil has order at least three, then "N!q