O jedenáctém a dvanáctém Hilbertově problému
On -class field towers of imaginary quadratic number fields
For a number field , let denote its Hilbert -class field, and put . We will determine all imaginary quadratic number fields such that is abelian or metacyclic, and we will give in terms of generators and relations.
On 2-rank of the ideal class groups of algebraic number fields.
On a Certain l-Adic Representation.
On a problem of Schinzel concerning principal divisors in arithmetic progressions
On a ratio between relative class numbers.
On an analogy to the Poisson summation formula for generalized Fourier transformation.
On Bilinear Structures on Divisor Class Groups
It is well known that duality theorems are of utmost importance for the arithmetic of local and global fields and that Brauer groups appear in this context unavoidably. The key word here is class field theory.In this paper we want to make evident that these topics play an important role in public key cryptopgraphy, too. Here the key words are Discrete Logarithm systems with bilinear structures.Almost all public key crypto systems used today based on discrete logarithms use the ideal class groups...
On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I
On Chinburg's second conjecture for abelian fields.
On extending a norm residue symbol.
On Iwasawa’s λ-invariant for certain -extensions
On K2 of Finite Dimensional Division Algebras Over Arithmetical Fields.
On knots in algebraic number theory.
On normal integral bases in ray class fields over imaginary quadratic fields
On -Ranks in the Class Field Tower Problem
Much recent progress in the 2-class field tower problem revolves around demonstrating infinite such towers for fields – in particular, quadratic fields – whose class groups have large 4-ranks. Generalizing to all primes, we use Golod-Safarevic-type inequalities to analyse the source of the -rank of the class group as a quantity of relevance in the -class field tower problem. We also make significant partial progress toward demonstrating that all real quadratic number fields whose class groups...
On -adic analytic families of Galois representations
On power residue characters of units and the representation of numbers by quadratic forms
On Ray Class Annihilators of Cyclotomic Fields.
On representations of the Weil group with bounded conductor.