On semi-local binomial units in cubic number fields.
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 truncated units in algebraic number fields of degree n ... 3.
On the asymptotic behavior of some counting functions
The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class group satisfies...
On the asymptotic behavior of some counting functions, II
The investigation of the counting function of the set of integral elements, in an algebraic number field, with factorizations of at most k different lengths gives rise to a combinatorial constant depending only on the class group of the number field and the integer k. In this paper the value of these constants, in case the class group is an elementary p-group, is estimated, and determined under additional conditions. In particular, it is proved that for elementary 2-groups these constants are equivalent...
On the canonical height for the algebraic unit group.
On the class number Q(√-p) modulo 16, for p ≡ 1 (mod 8) a prime
On the Construction of Independent units in cyclic or radical extensions.
On the distribution of algebraic numbers with prescribed factorization properties
On the existence of Minkowski units in totally real cyclic fields
Let be a totally real cyclic number field of degree that is the product of two distinct primes and such that the class number of the -th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for .
On the fundamental unit and class number of certain quadratic functin fields, I
On the fundamental units of some cubic orders generated by units
Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic polynomials...
On the group of circular units of any compositum of quadratic fields
On the Hilbert -class field tower of some imaginary biquadratic number fields
Let be an imaginary bicyclic biquadratic number field, where is an odd negative square-free integer and its second Hilbert -class field. Denote by the Galois group of . The purpose of this note is to investigate the Hilbert -class field tower of and then deduce the structure of .
On the iwasawa invariants of totally real number fields.
On the minimum of the unit lattice
On the multiplicative independence of binomial coefficients
On the number of solutions of linear equations in units of an algebraic number field.
On the quadratic character of some quadratic surds.
On the quantitative unit sum number problem-an application of the subspace theorem