Linearly Independent Zeros of Quadratic Forms over Number-Fields.
L'invariant de Witt de la forme Tr(x2).
Local conditions for global representations of quadratic forms
Local global theorems for diagonal forms of higher degree.
Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains
Let be a 2-dimensional normal excellent henselian local domain in which is invertible and let and be its fraction field and residue field respectively. Let be the set of rank 1 discrete valuations of corresponding to codimension 1 points of regular proper models of . We prove that a quadratic form over satisfies the local-global principle with respect to in the following two cases: (1) has rank 3 or 4; (2) has rank and , where is a complete discrete valuation ring with...
Local-global principle for Witt equivalence of function fields over global fields
We examine the conditions for two algebraic function fields over global fields to be Witt equivalent. We develop a criterion solving the problem which is analogous to the local-global principle for Witt equivalence of global fields obtained by R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland [12]. Subsequently, we derive some immediate consequences of this result. In particular we show that Witt equivalence of algebraic function fields (that have rational places) over global fields implies...
Localisation de formes quadratiques
Localisation de formes quadratiques. II
L'octogone régulier et la signature des formes quadratiques entières non singulières
La formule généralisant la loi de réciprocité quadratique de Legendre et exprimant le reste par huit de la signature d'une forme quadratique entière non dégénérée à l'aide d'une somme de Gauss est attribuée par Milnor à Milgram, la faisant remonter à Braun. Le formalisme de Witt la réduit au cas de dimension 1 que Chandrasekharan attribue à Cauchy et Kronecker. Braun soulignait que les preuves de ces formules nécessitent des moyens d'analyse. Une propriété métrique de l'octogone...
Lower bounds for the principal genus of definite binary quadratic forms.