On extensions of mixed motives.
In this article we give an introduction to mixed motives and sketch a couple of ways to construct examples.
On extensions of number fields obtained by specializing branched coverings.
On extensions of the maximal cyclotomic field having a given classical Galois group.
On extremal additive codes of length to
In this paper we consider the extremal even self-dual -additive codes. We give a complete classification for length . Under the hypothesis that at least two minimal words have the same support, we classify the codes of length and we show that in length such a code is equivalent to the unique -hermitian code with parameters [18,9,8]. We construct with the help of them some extremal -modular lattices.
On extremal h-bases A...
On extremal sets without coprimes
On extreme forms in dimension 8
A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for example out of the in dimension ). This is no longer the case in dimension : up to similarity, there...
On -maximal curves of genus .
On -thin sets
On Fabry's gap theorem
By combining Turán’s proof of Fabry’s gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.
On Factor Tables, with an Account of the Mode of Formation of the Factor Table for the Fourth Million [Book]
On factorization of integers with restrictions on the exponents.
On Fail-Rolle polynomials with few roots.
On families of 9-congruent elliptic curves
We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.
On families of counting functions of number fields and hyperbolic manifolds of dimensions two and three
On families of nonlinear recurrences related to digits.
On families of Pisot -sequences
On families of pure slope -functions.
On families of weakly dependent random variables
Let be a family of random independent k-element subsets of [n] = 1,2,...,n and let denote a family of ℓ-element subsets of [n] such that the event that S belongs to depends only on the edges of contained in S. Then, the edges of are ’weakly dependent’, say, the events that two given subsets S and T are in are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We also list...
On Fermat's equation with exponent 2p