On the number of subgroups of finite abelian groups
Journal de théorie des nombres de Bordeaux (1997)
- Volume: 9, Issue: 2, page 371-381
- ISSN: 1246-7405
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topIvić, Aleksandar. "On the number of subgroups of finite abelian groups." Journal de théorie des nombres de Bordeaux 9.2 (1997): 371-381. <http://eudml.org/doc/248010>.
@article{Ivić1997,
abstract = {Let\begin\{equation*\} T(x) = K\_1x \log ^2 x + K\_2x \log x + K\_3x + \Delta (x), \end\{equation*\}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 $\Delta (x)$ is the error term. It is proved that\begin\{equation*\} \int \_1^X \Delta ^2(x) dx \ll X^2 \log ^\{31/3\} X, \int \_1^X \Delta ^2 ( x) dx = \Omega (X^2 \log ^4 X).\end\{equation*\}},
author = {Ivić, Aleksandar},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {number of subgroups of finite abelian groups; asymptotic results on counting functions for algebraic structures},
language = {eng},
number = {2},
pages = {371-381},
publisher = {Université Bordeaux I},
title = {On the number of subgroups of finite abelian groups},
url = {http://eudml.org/doc/248010},
volume = {9},
year = {1997},
}
TY - JOUR
AU - Ivić, Aleksandar
TI - On the number of subgroups of finite abelian groups
JO - Journal de théorie des nombres de Bordeaux
PY - 1997
PB - Université Bordeaux I
VL - 9
IS - 2
SP - 371
EP - 381
AB - Let\begin{equation*} T(x) = K_1x \log ^2 x + K_2x \log x + K_3x + \Delta (x), \end{equation*}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 $\Delta (x)$ is the error term. It is proved that\begin{equation*} \int _1^X \Delta ^2(x) dx \ll X^2 \log ^{31/3} X, \int _1^X \Delta ^2 ( x) dx = \Omega (X^2 \log ^4 X).\end{equation*}
LA - eng
KW - number of subgroups of finite abelian groups; asymptotic results on counting functions for algebraic structures
UR - http://eudml.org/doc/248010
ER -
References
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