The non-symmetric divisor function $\tau \left( {1,1,2;n} \right)$ in arithmetic progression |
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| Author |
Department of Computer Algebra and Discrete Mathematics,Institute of Mathematics, Economics and Mechanics,Odessa National University,Dvoryanskaya Str. 2,65000 Odessa,Ukraine
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| Abstract |
For the function $\tau \left( {1,1,2;n} \right)$ that defines
the number of different representations of $n$ in the form $n = n_1
n_2 n_3^2 $, we construct an asymptotic formula of its
summatory function in arithmetic progression, nontrivial for
$q \ll x^{\frac{14}{27}}$, where $q$ is the difference of the progression.
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| Keywords |
function , number of different representations , asymptotic formula, summatory function, arithmetic progression, difference of the progression
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| DOI |
doi:10.30970/ms.18.2.115-124
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Reference |
1. Heath-Brown D.R. The divisor function $d_3(n)$ in arithmetic progressions // Acta Arith. XLVII (1986), P.~29-56.
2. Birch B.J. and Bombieri E. Appendix: On some exponential sums // Annals of Math. 121(1985), P. 345-350. 3. R.A. Smith, On $n$-dimensional Kloosterman sums // J.~Number Theory~11 (1979), p.~324-343. |
| Pages |
115-124
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| Volume |
18
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| Issue |
2
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| Year |
2002
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| Journal |
Matematychni Studii
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| Full text of paper | |
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