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Moments of the probability density functions of error terms in divisor problems


Authors: Yuk-Kam Lau and Kai-Man Tsang
Journal: Proc. Amer. Math. Soc. 133 (2005), 1283-1290
MSC (2000): Primary 11N60
DOI: https://doi.org/10.1090/S0002-9939-04-07825-6
Published electronically: December 15, 2004
MathSciNet review: 2111933
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Abstract | References | Similar Articles | Additional Information

Abstract: We derive an explicit formula for the moments of the probability density function of a class of functions. An application of this shows that the density function of the error term in the Pilz divisor problem is asymmetric.


References [Enhancements On Off] (What's this?)

  • 1. P.M. Bleher, Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems, Duke Math. J. 70 (1993), 655-682. MR 1224102 (94g:11082)
  • 2. P.M. Bleher, Z. Cheng, F.J. Dyson and J.L. Lebowitz, Distribution of the error term for the number of lattice points inside a shifted circle, Commun. Math. Phys. 154 (1991), 433-469. MR 1224087 (94g:11081)
  • 3. D.R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, Acta Arith. 60 (1992), 389-415. MR 1159354 (93e:11114)
  • 4. Y.-K. Lau, On the existence of limiting distributions of some number-theoretic error terms, J. Number Theory 94 (2002), 359-374. MR 1916279 (2003e:11104)
  • 5. K.-M. Tsang, Higher-power moments of $\Delta(x)$, $E(t)$and $P(x)$, Proc. London Math. Soc. (3) 65 (1992), 65-84. MR 1162488 (93c:11082)
  • 6. W. Zhai, On higher-power moments of $\Delta(x)$ II, Acta Arith. 114 (2004), 35-54. MR 2067871

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Additional Information

Yuk-Kam Lau
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: yklau@maths.hku.hk

Kai-Man Tsang
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: kmtsang@maths.hku.hk

DOI: https://doi.org/10.1090/S0002-9939-04-07825-6
Received by editor(s): November 11, 2003
Published electronically: December 15, 2004
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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