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Proceedings of the American Mathematical Society

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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: 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.


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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.