A Symmetric Form of the Mean Value Involving Non-Isomorphic Abelian Groups

Let a(n) be the number of non-isomorphic abelian groups of order n. In this paper, we study a symmetric form of the average value with respect to a(n) and prove an asymptotic formula. Furthermore, we study an analogue of the well-known Titchmarsh divisor problem involving a(n).

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Symmetry (Basel) 2022-09, Vol.14 (9), p.1755
Hauptverfasser:	Fan, Haihong, Zhai, Wenguang
Format:	Artikel
Sprache:	eng
Schlagworte:	asymptotic formula Bombieri–Vinogradov theorem finite abelian group Group theory Mathematical functions Prime numbers symmetric average value Titchmarsh divisor problem
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	Let a(n) be the number of non-isomorphic abelian groups of order n. In this paper, we study a symmetric form of the average value with respect to a(n) and prove an asymptotic formula. Furthermore, we study an analogue of the well-known Titchmarsh divisor problem involving a(n).
ISSN:	2073-8994 2073-8994
DOI:	10.3390/sym14091755