No CrossRef data available.
Article contents
The Dirichlet Divisor Problem of Arithmetic Progressions
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2016
References
[1]
Davenport, H., Multiplicative number theory. Second edition. Graduate Texts in Mathematics 74, Springer-Verlag, New York, 1980.Google Scholar
[2]
Estermann, T., On Kloosterman's sum.
Mathematika
8(1961), 83–86. http://dx.doi.org/10.1112/S0025579300002187
Google Scholar
[3]
Friedlander, J. B. and Iwaniec, H., The divisor problem for arithmetic progressions.
ActaArith.
45(1985), 273–277.Google Scholar
[4]
Heath-Brown, D. R., The fourth power moment of the Riemann zeta-function.
Proc. London Math. Soc.
38(1979), no. 3, 385–422. http://dx.doi.org/10.1112/plms/s3-38.3.385
Google Scholar
[5]
Hooley, C., An asymptotic formula in the theory of numbers.
Proc. London Math. Soc.
7(1957), no. 3, 396–412. http://dx.doi.org/10.1112/plms/s3-7.1.396
Google Scholar
[6]
Hooley, C., On the number of divisors of quadratic polynomials.
ActaMath.
110(1963), 97–114. http://dx.doi.org/10.1007/BF02391856
Google Scholar
[7]
Hua, L. K., Introduction to number theory.
Springer-Verlag, Berlin, 1982 (translated from Chinese by P. Shiu).Google Scholar
[8]
Liu, H.-Q., On the estimates for double exponential sums.
ActaArith.
129(2007), 203–247. http://dx.doi.org/10.4064/aa129-3-1
Google Scholar
[9]
Liu, H.-Q., Barban-Davenport-Halberstam average sum and the exceptional zero of L-functions.
J. Number Theory,
128(2008), 1011–1043. http://dx.doi.org/10.1016/j.jnt.2007.08.003
Google Scholar
[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]
Smith, R. A., The generalized divisor problem over arithmetic progressions.
Math. Ann.
260(1982), 255–268. http://dx.doi.org/10.1007/BF01457239
Google Scholar
[12]
Titchmarsh, E. C., The theory of functions.
Oxford University Press, Oxford, 1958.Google Scholar
You have
Access