On the number of subgroups of finite abelian groups
Aleksandar Ivić
Journal de Théorie des Nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 371-381.

Soit T(x)=K 1 xlog 2 x+K 2 xlogx+K 3 x+Δ(x), où T(x) désigne le nombre de sous groupes des groupes abéliens dont l’ordre n’excède pas x et dont le rang n’excède pas 2, et Δ(x) est le terme d’erreur. On démontre que ∫ 1 X Δ 2 (x)dx≪X 2 log 31/3 X,∫ 1 X Δ 2 (x)dx=Ω(X 2 log 4 X).

Let T(x)=K 1 xlog 2 x+K 2 xlogx+K 3 x+Δ(x), where T(x) denotes the number of subgroups of all abelian groups whose order does not exceed x and whose rank does not exceed 2, and Δ(x) is the error term. It is proved that ∫ 1 X Δ 2 (x)dx≪X 2 log 31/3 X,∫ 1 X Δ 2 (x)dx=Ω(X 2 log 4 X).

DOI : https://doi.org/10.5802/jtnb.208
Classification : 11N45,  11L07,  20K01,  20K27 
@article{JTNB_1997__9_2_371_0,
     author = {Ivi\'c, Aleksandar},
     title = {On the number of subgroups of finite abelian groups},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {371--381},
     publisher = {Universit\'e Bordeaux I},
     volume = {9},
     number = {2},
     year = {1997},
     doi = {10.5802/jtnb.208},
     zbl = {0905.11040},
     mrnumber = {1617404},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.208/}
}
Aleksandar Ivić. On the number of subgroups of finite abelian groups. Journal de Théorie des Nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 371-381. doi : 10.5802/jtnb.208. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.208/

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