The number of finite non-isomorphic abelian groups in mean square.
Ivić, Aleksandar
HAL, hal-01104704 / Harvested from HAL
Text on HAL
Let $\Delta(x)=\sum_{n\leq x}a(n)-\sum_{j=1}^6 c_jx^{1/j}$ denote the error term in the abelian group problem. Using zeta-function methods it is proved that $$\int_1^X\Delta^2(x)\,dx~<\!\!<~ X^{39/29} \log^2X$$ where the exponent $39/29=1.344827\ldots$ is close to the best possible exponent $4/3$ in this problem.
Publié le : 1986-07-04
Classification:  number of non-isomorphic abelian groups,  mean square estimates,  power moments of the zeta-function.,  [MATH]Mathematics [math] 
@article{hal-01104704,
     author = {Ivi\'c, Aleksandar},
     title = {The number of finite non-isomorphic abelian groups in mean square.},
     journal = {HAL},
     volume = {1986},
     number = {0},
     year = {1986},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01104704}
}

Ivić, Aleksandar. The number of finite non-isomorphic abelian groups in mean square.. HAL, Tome 1986 (1986) no. 0, . http://gdmltest.u-ga.fr/item/hal-01104704/