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Moments of the probability density functions of error terms in divisor problems
Author(s):
Yuk-Kam
Lau;
Kai-Man
Tsang
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1283-1290.
MSC (2000):
Primary 11N60
Posted:
December 15, 2004
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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:
-
- 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)
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, and , Proc. London Math. Soc. (3) 65 (1992), 65-84. MR 1162488 (93c:11082) - 6.
- W. Zhai, On higher-power moments of
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:
10.1090/S0002-9939-04-07825-6
PII:
S 0002-9939(04)07825-6
Received by editor(s):
November 11, 2003
Posted:
December 15, 2004
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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