Geodesic
The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt} (p + 1)$
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 581-591.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We study the irreducibility of the Dirichlet polynomial $P_G(s)$ when $G$ is the alternating group on $p + 1$ elements with $p$ prime and we prove that $P_G(s)$ is irreducible for infinitely many choiches of $p$.
Si studia l'irriducibilità del polinomio di Dirichlet $P_G(s)$ nel caso in cui $G$ sia il gruppo alterno di grado $p + 1$, con $p$ primo, e si prova che $P_G(s)$ è irriducibile per infinite scelte di $p$. 
@article{BUMI_2007_8_10B_3_a6,
     author = {Massa, Marilena},
     title = {The {Probabilistic} {Zeta} {Function} of the {Alternating} {Group} $\operatorname{Alt} (p + 1)$},
     journal = {Bollettino della Unione matematica italiana},
     pages = {581--591},
     publisher = {mathdoc},
     volume = {Ser. 8, 10B},
     number = {3},
     year = {2007},
     zbl = {1167.20317},
     mrnumber = {2351530},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a6/}
}
TY  - JOUR
AU  - Massa, Marilena
TI  - The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt} (p + 1)$
JO  - Bollettino della Unione matematica italiana
PY  - 2007
SP  - 581
EP  - 591
VL  - 10B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a6/
LA  - en
ID  - BUMI_2007_8_10B_3_a6
ER  - 
%0 Journal Article
%A Massa, Marilena
%T The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt} (p + 1)$
%J Bollettino della Unione matematica italiana
%D 2007
%P 581-591
%V 10B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a6/
%G en
%F BUMI_2007_8_10B_3_a6
Massa, Marilena. The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt} (p + 1)$. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 581-591. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a6/

[1] K. Alladi - R. Solomon - A. Turull, Finite simple groups of bounded subgroup chain length, J. Algebra, 231 (2000), 374-386. | DOI | MR | Zbl

[2] Nigel Boston, A probabilistic generalization of the Riemann zeta function, Analytic number theory, Vol. 1 (Allerton Park, IL, 1995) 138 (1996), 155-162. | MR | Zbl

[3] Kenneth S. Brown, The coset poset and probabilistic zeta function of a finite group, J. Algebra, 225, no. 2 (2000), 989-1012. | DOI | MR | Zbl

[4] Erika Damian - Andrea LUCCHINI - Fiorenza MORINI, Some properties of the probabilistic zeta function of finite simple groups, Pacific J. Math., 215 (2004), 3-14. | DOI | MR | Zbl

[5] John D. Dixon - Brian Mortimer, Permutation groups, Graduate Texts in Mathematics, vol. 163, Springer-Verlag, New York, 1996. | DOI | MR | Zbl

[6] Philip Hall, The eulerian functions of a group, Quart. J. Math., no. 7 (1936), 134-151. | Zbl

[7] G. H. Hardy - E. M. Wright, An introduction to the theory of numbers, fifth ed., The Clarendon Press Oxford University Press, New York, 1979. | MR | Zbl

[8] Avinoam Mann, Positively finitely generated groups, Forum Math. 8, no. 4 (1996), 429-459. | fulltext EuDML | DOI | MR | Zbl

[9] P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, New York, 1989, 23-24. | DOI | MR

[10] John Shareshian, On the probabilistic zeta function for finite groups, J. Algebra 210, no. 2 (1998), 703-707. | DOI | MR | Zbl