On the congruence subgroup problem
On the congruences and
On the congruence-subgroup problem for some anisotropic algebraic groups over number fields.
On the Conjecture of Birch and Swinnerton-Dyer
On the conjecture of Birch and Swinnerton-Dyer for abelian varieties over function fields in characteristic p > 0.
On the conjecture of Lichtenbaum and of Chinburg over function fields.
On the conjectures of Birch and Swinnerton-Dyer and a geometric analog
On the conjectures of Mordell and Lang in positive characteristics.
On the conjectures of Rauzy and Shallit for infinite words
We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.
On the constant factor in Vinogradov's Mean Value Theorem
On the constant β(k) in Rosser's sieve
On the construction of dense lattices with a given automorphisms group
We consider the problem of constructing dense lattices in with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions , we exhibit a finite set of lattices that come with an automorphisms group of size , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...
On the Construction of Galois Extensions of Function Fields and Number Fields.
On the Construction of Independent units in cyclic or radical extensions.
On the continued fractions of quadratic surds
On the convergence to 0 of mₙξmod 1
We show that for any irrational number α and a sequence of integers such that , there exists a continuous measure μ on the circle such that . This implies that any rigidity sequence of any ergodic transformation is a rigidity sequence for some weakly mixing dynamical system. On the other hand, we show that for any α ∈ ℝ - ℚ, there exists a sequence of integers such that and such that is dense on the circle if and only if θ ∉ ℚα + ℚ.
On the converse of Wolstenholme's Theorem
On the coprimality of certain multiplicative functions
On the Coprimality of Some Arithmetic Functions
On the coprimality of values of Euler's function at consecutive integers.