Exponential sums and the abelian group problem
Liu, H.-Q.
Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, p. 113-129 / Harvested from Project Euclid
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We give new estimates for multiple exponential sums, which infers $$A(x)=C_1x+C_2x^{1/2}+C_3x^{1/3}+O(x^{1/4}e^{V(x)}), V(x)=\frac{1}{\sqrt{3}}(L\log{L})^{1/2}+O((L\log{L})^{1/2}),$$ where $L=\log{x}$, $A(x)$ is the number of non-isomorphic abelian groups of orders $\leq{x}$, and $x$ is large.
Publié le : 2010-03-15
Classification:  Abelian groups,  exponential sums,  11L06,  11M20 
@article{1277811635,
     author = {Liu, H.-Q.},
     title = {Exponential sums and the abelian group problem},
     journal = {Funct. Approx. Comment. Math.},
     volume = {42},
     number = {1},
     year = {2010},
     pages = { 113-129},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1277811635}
}

Liu, H.-Q. Exponential sums and the abelian group problem. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp.  113-129. http://gdmltest.u-ga.fr/item/1277811635/