caa a22 4500 475740378 CHVBK 20180406123458.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/BF02674561 doi (NATIONALLICENCE)springer-10.1007/BF02674561 Pavlov A. V. A. Steklov Mathematics Institute, Russian Academy of Sciences, USSR aut On the ingham divisor problem [Elektronische Daten] [A. Pavlov] 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 \g3\s>0 the following relation holds: $$\sum\limits_{n \leqslant x} {r(n)} r(n + 1)F(n) = A_1 xln^{\text{2}} x + A_{\text{2}} xlnx + A_{\text{3}} x + O(x^{5/6 + \varepsilon } + x^{1 - \alpha /6 + \varepsilon } ), x \to \infty .$$ . Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA 1\s>0. Kluwer Academic/Plenum Publishers, 2000 Ingham divisor nationallicence Ingham's equality nationallicence arithmetical function nationallicence Heath-Brown theorem nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/3(2000-09-01), 370-377 0001-4346 68:3<370 2000 68 11006 https://doi.org/10.1007/BF02674561 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02674561 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pavlov A. V. A. Steklov Mathematics Institute, Russian Academy of Sciences, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/3(2000-09-01), 370-377 0001-4346 68:3<370 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer