Absolute stable rank and Witt cancellation for noncommutative rings.
Abstract Grothendieck rings
Action of Hecke Operator T(p) on Theta Series.
Addendum to: On volumes of arithmetic quotients of SO (1, n)
There are errors in the proof of uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.
Additive structure of multiplicative subgroups of fields and Galois theory.
Alcune osservazioni sulle forme trilineari
Si studiano, nell'ambito della teoria delle forme trilineari, le cosidette -forme simmetriche, pervenendo ad un teorema di struttura utile per una possibile classificazione, ancora inesistente, di tali -forme.
Algebraic Classification of Linking Pairings on 3-Manifolds.
Algebraic -theory and sums-of-squares formulas.
Algebraic K-Theory and Quadratic Forms.
Algebraic systems of quadratic forms of number fields and function fields.
Algorithme de multiplicativité des sommes de carrés
Algorithms for quadratic forms over real function fields
This paper presents algorithms for quadratic forms over a formally real algebraic function field K of one variable over a fixed real closed field k. The algorithms introduced in the paper solve the following problems: test whether an element is a square, respectively a local square, compute Witt index of a quadratic form and test if a form is isotropic/hyperbolic. Finally, we remark on a method for testing whether two function fields are Witt equivalent.
Almost regular quaternary quadratic forms
We investigate the almost regular positive definite integral quaternary quadratic forms. In particular, we show that every such form is -anisotropic for at most one prime number . Moreover, for a prime there is an almost regular -anisotropic quaternary quadratic form if and only if . We also study the genera containing some almost regular -anisotropic quaternary form. We show several finiteness results concerning the families of these genera and give effective criteria for almost regularity....
An Abstract Treatment of the Module of Quadratic Forms over a Semi-local Ring.
An alternative proof of Scheiderer's theorem on the Hasse principle for principal homogeneous spaces.
An analogue of Pfister's local-global principle in the burnside ring
Let be a Galois extension with Galois group . We study the set of -linear combinations of characters in the Burnside ring which give rise to -linear combinations of trace forms of subextensions of which are trivial in the Witt ring W of . In particular, we prove that the torsion subgroup of coincides with the kernel of the total signature homomorphism.
An application of dihedral fields to representations of primes by binary quadratic forms
An arithmetic formula of Liouville
An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.
An arithmetic problem on the sums of three squares
An arithmetical property of quadratic forms.