On index formulas of Siegel units in a ring class field
On integer solutions to x² - dy² = 1, z² - 2dy² =1
On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
On Kronecker équivalence of algebraic number fields.
On K-Stage Euclidean algorithms for Galois extensions of Q.
On Minkowski units constructed by special values of Siegel modular functions
Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field of modulo . Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group for the special values. Futhermore we construct the full unit group of using modular and circular units under the GRH.
On natural numbers having unique factorization in a quadratic number field, II
On power residue characters of units and the representation of numbers by quadratic forms
On relations between units of normal algebraic number fields and their subfields
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