A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
A lower bound on the number of finite simple groups.
A note on certain semigroups of algebraic numbers
The cross number κ(a) can be defined for any element a of a Krull monoid. The property κ(a) = 1 is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, κ(a) ∈ ℤ, is still unknown, but it does define a semigroup which may be interesting in its own right. This paper studies some arithmetic(divisor theory) and analytic(distribution of elements with a given norm) properties of that semigroup and a related semigroup of ideals....
A Note on the Growth of Davenport's constant.
An asymptotic formula in the theory of numbers
Arithmetical Semigroups III: Elements With Prime Factors in Residue Classes.
Asymptotic density in combined number systems.
Carmichael's lambda function
Closed orbits of -extension of ergodic toral automorphisms.
Comparing the number of abelian groups and of semisimple rings of a given order
Comportement des fonctions arithmétiques complexes, multiplicatives, à valeurs dans le disque
Conjugacy class lengths of metanilpotent groups
Counting invertible matrices and uniform distribution
Consider the group over the ring of algebraic integers of a number field . Define the height of a matrix to be the maximum over all the conjugates of its entries in absolute value. Let be the number of matrices in with height bounded by . We determine the asymptotic behaviour of as goes to infinity including an error term,with being the degree of . The constant involves the discriminant of , an integral depending only on the signature of , and the value of the Dedekind zeta function...
Counting irreducible polynomials over finite fields
In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: where denotes the number of monic irreducible polynomials in with norm .
Counting -groups and nilpotent groups
Counting solutions of decomposable form equations
Covering abelian groups with cyclic subsets.
Densities for 3-class ranks in certain cubic extensions.
Dichte von Frobeniuskörpern bei fixiertem Kernkörper.
Die Wertevertailung Der Anzahl Der Nicht-Isomorphen Abelschen Gruppen Endlicher Ordnung Und Ein Verwandtes Zahlenteoretisches Problem