On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On Schertz's class number formula related to elliptic units for some non-Galois extensions
On semi-local binomial units in cubic number fields.
On sequences of algebraic integers in pure extensions of prime degree
On shifted primes
On Shioda's problem about Jacobi sums
On Shioda's problem about Jacobi sums II
On Siegel Zeros of Hecke-Landau Zeta-Functions.
On Siegel's Lemma.
On Sign Determinations in Real Algebraic Number Fields.
On singular moduli.
On singular moduli for rank 2 Drinfeld modules
On solutions of the equation Xⁿ + Yⁿ = BZⁿ with prime n|BZ
On Solvable Number Fields.
On some class-fields related to primes of type x2 + 32y2.
On some estimates in the theory of ζ(8,χ) - functions
On some imaginary triquadratic number fields with or
Let be a square free integer and . In the present work we determine all the fields such that the -class group, , of is of type or .
On some issues concerning polynomial cycles
We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain of positive characteristic (for ) or for any Dedekind domain of positive characteristic (but only for ), we give a closed formula for a set of all possible cycle-lengths for polynomial mappings in . Then we give a new property of sets , which refutes a kind of conjecture posed by W. Narkiewicz.
On some metabelian 2-groups and applications I
Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem for the 2-ideal classes of some fields k satisfying the condition , where is the second Hilbert 2-class field of k.
On some new congruences for generalized Bernoulli numbers