Ingham divisor problem with square-free numbers |
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Authors: | D V Goryashin |
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Institution: | 1.Faculty of Mechanics and Mathematics,Moscow State University,Leninskie Gory, Moscow,Russia |
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Abstract: | For the number N(x) of solutions to the equation aq − bc = 1 in positive integers a, b, c and square-free numbers q satisfying the condition aq ≤ x the asymptotic formula
$N\left( x \right) = \sum\limits_{n \leqslant x} {2^{\omega \left( n \right)} \tau \left( {n - 1} \right) = \xi _0 x\ln ^2 x + \xi _1 x\ln x + \xi _2 x + O\left( {x^{{5 \mathord{\left/
{\vphantom {5 {6 + \varepsilon }}} \right.
\kern-\nulldelimiterspace} {6 + \varepsilon }}} } \right)}$N\left( x \right) = \sum\limits_{n \leqslant x} {2^{\omega \left( n \right)} \tau \left( {n - 1} \right) = \xi _0 x\ln ^2 x + \xi _1 x\ln x + \xi _2 x + O\left( {x^{{5 \mathord{\left/
{\vphantom {5 {6 + \varepsilon }}} \right.
\kern-\nulldelimiterspace} {6 + \varepsilon }}} } \right)} |
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Keywords: | |
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