Statistiques sur
Subgroups of finite index in nilpotent groups.
The asymptotic behaviour of the counting functions of Ω-sets in arithmetical semigroups
We consider an axiomatically-defined class of arithmetical semigroups that we call simple L-semigroups. This class includes all generalized Hilbert semigroups, in particular the semigroup of non-zero integers in any algebraic number field. We show, for all positive integers k, that the counting function of the set of elements with at most k distinct factorization lengths in such a semigroup has oscillations of logarithmic frequency and size for some M>0. More generally, we show a result on...
The average order of a permutation.
The density of representation degrees
For a group and a positive real number , define to be the number of integers less than which are dimensions of irreducible complex representations of . We study the asymptotics of for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups in characteristic zero, showing that either there exists such that for all large , or is virtually abelian (in which case is bounded).
The distribution of group structures on elliptic curves over finite prime fields.
The number of commutative semigroups of order N.
Théorèmes de densité dans
Trivial Selmer groups and even partitions of a graph.
Übe die Anzahl Abelscher Gruppen gegebener Ordnung. II.
Über die Anzahl Abelscher Gruppen gegebener Ordnung. I.
Über die Verteilung der pythagoräischen Dreiecke
Über die Verteilung ganzer Zahlen mit ausgezeichneten Eigenschaften der Faktorzerlegung in algebraischen Zahlkörpern
Weighted Erdős-Kac type theorem over quadratic field in short intervals
Let be a quadratic field over the rational field and be the number of nonzero integral ideals with norm . We establish Erdős-Kac type theorems weighted by and of quadratic field in short intervals with . We also get asymptotic formulae for the average behavior of and in short intervals.
When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently
Zeta functions and counting finite -groups.
Zur Anzahl unitärer Faktoren abelscher Gruppen
Об асимптотической формуле для числа абелевых групп, порядки которых не превосходят
Свёртки рядов Дирихле с коэффициентами Фурье параболических форм веса 0