Geodesic
The Dirichlet Divisor Problem of Arithmetic Progressions
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 592-598

Voir la notice de l'article provenant de la source Cambridge University Press

We present an elementary method for studying the problem of getting an asymptotic formula that is better than Hooley's and Heath-Brown's results for certain cases.
DOI : 10.4153/CMB-2016-029-5
Mots-clés : 11L07, 11B83, Dirichlet divisor problem, arithmetic progression 
Liu, H. Q. The Dirichlet Divisor Problem of Arithmetic Progressions. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 592-598. doi: 10.4153/CMB-2016-029-5
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[1] [1] Davenport, H., Multiplicative number theory. Second edition. Graduate Texts in Mathematics 74, Springer-Verlag, New York, 1980. Google Scholar

[2] [2] Estermann, T., On Kloosterman's sum. Mathematika 8(1961), 83–86. Google Scholar | DOI

[3] [3] Friedlander, J. B. and Iwaniec, H., The divisor problem for arithmetic progressions. ActaArith. 45(1985), 273–277. Google Scholar

[4] [4] Heath-Brown, D. R., The fourth power moment of the Riemann zeta-function. Proc. London Math. Soc. 38(1979), no. 3, 385–422. Google Scholar | DOI

[5] [5] Hooley, C., An asymptotic formula in the theory of numbers. Proc. London Math. Soc. 7(1957), no. 3, 396–412. Google Scholar | DOI

[6] [6] Hooley, C., On the number of divisors of quadratic polynomials. ActaMath. 110(1963), 97–114. Google Scholar | DOI

[7] [7] Hua, L. K., Introduction to number theory. Springer-Verlag, Berlin, 1982 (translated from Chinese by P. Shiu). Google Scholar

[8] [8] Liu, H.-Q., On the estimates for double exponential sums. ActaArith. 129(2007), 203–247. Google Scholar | DOI

[9] [9] Liu, H.-Q., Barban-Davenport-Halberstam average sum and the exceptional zero of L-functions. J. Number Theory, 128(2008), 1011–1043. Google Scholar | DOI

[10] [10] Montgomery, H. L. and Vaughan, R. C., The distribution of square-free numbers. In: Recent progress in analytic number theory, I. Academic Press, London, 1981, pp. 247–256. Google Scholar

[11] [11] Smith, R. A., The generalized divisor problem over arithmetic progressions. Math. Ann. 260(1982), 255–268. Google Scholar | DOI

[12] [12] Titchmarsh, E. C., The theory of functions. Oxford University Press, Oxford, 1958. Google Scholar

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