On nonary cubic forms.
On nonary cubic forms: II.
On nonary cubic forms: III.
On orthogonal decomposition of homogeneous polynomials
On the classification of 3-dimensional non-associative division algebras over -adic fields
Let be a prime and a -adic field (a finite extension of the field of -adic numbers ). We employ the main results in [12] and the arithmetic of elliptic curves over to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over to the classification of ternary cubic forms over (up to equivalence) with no non-trivial zeros over . We give an explicit solution to the latter problem, which we then relate to the reduction type of the jacobian...
On the fractional parts of cubic forms
On the number of equivalence classes of binary forms of given degree and given discriminant
On the Poincaré series for diagonal forms over algebraic number fields
On the properties of invariants of forms.
On the Representation of Integers by Binary Cubic Forms of Positive Discriminant.
On the representation of integers by binary cubic forms of positive discriminant (Erratum).
On the representation of integers by certain binary cubic and biquadratic forms
On weak automorphs of binary forms over an arbitrary field [Book]
On zeros of diagonal forms over p-adic fields
On zeros of forms over local fields
Pairs of cubic forms in many variables
Petites solutions des congruences
Random Thue and Fermat equations
We consider Thue equations of the form , and assuming the truth of the abc-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle. A similar conclusion holds true for Fermat equations of degree at least six.
Real Zeros of Positive Semidefinite Forms. I.
Relations between Elements and p·1 for a Prime p
For any positive power n of a prime p we find a complete set of generating relations between the elements [r] = rⁿ - r and p·1 of a unitary commutative ring.