On the ingham divisor problem |
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Authors: | A. I. Pavlov |
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Affiliation: | (1) V. A. Steklov Mathematics Institute, Russian Academy of Sciences, USSR |
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Abstract: | The main result of this paper is the following theorem. Suppose thatτ(n) = ∑ d|n l and the arithmetical functionF satisfies the following conditions: 1) | the functionF is multiplicative; | 2) | ifF(n) = ∑ d|n f(d), then there exists an α>0 such that the relationf(n)=O(n −α) holds asn→∞. | Then there exist constantsA 1,A 2, andA 3 such that for any fixed g3s>0 the following relation holds:. Moreover, if for any primep the inequality vbf(p)vbs<1 holds and the functionF is strongly multiplicative, thenA 1s>0. Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 429–438, September, 2000. |
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Keywords: | Ingham divisor Ingham’ s equality arithmetical function Heath-Brown theorem |
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