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On the number of subgroups of finite abelian groups

Aleksandar Ivić (1997)

Journal de théorie des nombres de Bordeaux

Let T ( x ) = K 1 x log 2 x + K 2 x log x + 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 ) d x X 2 log 31 / 3 X , 1 X Δ 2 ( x ) d x = Ω ( X 2 log 4 X ) .

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