On explicit relations between cyclotomic numbers
On extending a norm residue symbol.
On extensions of 1 chains
On extensions of number fields obtained by specializing branched coverings.
On extensions of the maximal cyclotomic field having a given classical Galois group.
On families of counting functions of number fields and hyperbolic manifolds of dimensions two and three
On families of Pisot -sequences
On Fermat's last theorem.
On Fermat's last theorem. VII.
On finite linear groups stable under Galois operation.
On first layers of ℤₚ-extensions II
On Fröhlich's Conjecture for Rings of Integers of Tame Extensions.
On galois automorphisms of the fundamental group of the projective line minus three points.
On Galois groups of p-closed algebraic number fields with restricted ramification II.
On Galois groups of p-closed algebraic number fields with restricted ramification.
On Galois representations arising from towers of coverings of P1 ... .
On Galois representations associated to Hilbert modular forms.
On Galois structure of the integers in cyclic extensions of local number fields
Let be a rational prime, be a finite extension of the field of -adic numbers, and let be a totally ramified cyclic extension of degree . Restrict the first ramification number of to about half of its possible values, where denotes the absolute ramification index of . Under this loose condition, we explicitly determine the -module structure of the ring of integers of , where denotes the -adic integers and denotes the Galois group Gal. In the process of determining this structure,...
On gaps in Rényi -expansions of unity for an algebraic number
Let be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi -expansion of unity which controls the set of -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in are shown to exhibit a “gappiness” asymptotically bounded above by , where is the Mahler measure of . The proof of this result provides in a natural way a new classification of algebraic numbers with classes called Q...
On Garcia numbers.