### Radicals and units in Ramanujan's work

Bruce C. Berndt, Heng Huat Chan, Liang-Cheng Zhang (1998)

Acta Arithmetica

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Bruce C. Berndt, Heng Huat Chan, Liang-Cheng Zhang (1998)

Acta Arithmetica

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Khusnutdinova, N.V. (2001)

Sibirskij Matematicheskij Zhurnal

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Bruce C. Berndt, Heng Huat Chan, Liang-Cheng Zhang (1995)

Acta Arithmetica

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Borovkov, A.A. (2002)

Sibirskij Matematicheskij Zhurnal

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Ivanchov, N.I., Pabyrivska, N.V. (2002)

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Egorov, A.A., Korobkov, M.V. (2001)

Sibirskij Matematicheskij Zhurnal

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Pyatkov, S.G., Abasheeva, N.L. (2000)

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Mikhajlov, G.A., Burmistrov, A.V. (2000)

Siberian Mathematical Journal

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Hong-Quan Liu (1993)

Acta Arithmetica

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1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, $A\left(x\right)=C\u2081x+C\u2082{x}^{1/2}+C\u2083{x}^{1/3}+O\left({x}^{50/199+\epsilon}\right)$, where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented...

Dragomir, Sever S. (2007)

Banach Journal of Mathematical Analysis [electronic only]

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Korotkov, V.B. (2000)

Sibirskij Matematicheskij Zhurnal

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Laevskij, Yu.M. (2000)

Siberian Mathematical Journal

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